0580.C4.6.04 — angle sum of a triangle = 180° and angl.: past paper questions

Real questions on 0580.c4.6.04 — angle sum of a triangle = 180° and angl.

The newest 20 of 24 written questions. Open one to see it on the real paper.

1. 0580/42 · May/June 2026 · Q1[2]
   1 [Diagram: Triangle $ABC$ with $AB=AC$ indicated by tick marks. Angle $A$ is $30^{\circ }$. Angle $C$ is $x^{\circ }$. Labelled "NOT TO SCALE"] Triangle $ABC$ is isosceles with $AB=AC$. Find the value of $x$.See it on the paper →
2. 0580/01 · Specimen 2025 · Q10a[2]

   2-mark “Find” question — its maths and diagrams are best seen on the paper.

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3. 0580/01 · Specimen 2025 · Q10b[2]

   2-mark “Find” question — its maths and diagrams are best seen on the paper.

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4. 0580/01 · Specimen 2025 · Q10c[2]

   2-mark “Find” question — its maths and diagrams are best seen on the paper.

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5. 0580/11 · October/November 2025 · Q15[3]
   [Diagram: Triangle $ABD$ with $AB=BD$ (indicated by tick marks). Angle $ADB=x^{\circ }$. Line $ABC$ is a straight line. Angle $DBC=140^{\circ }$. NOT TO SCALE.] $ABC$ is a straight line and $ABD$ is an isosceles triangle. Work out the value of $x$. $x=$See it on the paper →
6. 0580/13 · October/November 2025 · Q10b[1]
   The diagram shows an isosceles triangle between a pair of parallel lines. [Diagram: Two parallel horizontal lines with arrows pointing right. An isosceles triangle is positioned between them. The top vertex is on the upper line, and the base is on the lower line. The angle between the upper line and the left side of th...See it on the paper →
7. 0580/23 · October/November 2025 · Q1[2]
   1 [Diagram: An isosceles triangle, NOT TO SCALE. The two equal sides (marked with tick marks) meet at the top vertex, which has an interior angle of $x^{\circ }$. The base angles are equal; the right base angle is marked as $25^{\circ }$.] The diagram shows an isosceles triangle. Find the value of $x$. $x=$See it on the paper →
8. 0580/23 · October/November 2025 · Q10a[3]
   [Diagram: A right-angled triangle $ABC$ with the right angle at $A$. The side $AB$ is horizontal with length $8\text{ cm}$. The side $AC$ is vertical. The hypotenuse $BC$ has length $11\text{ cm}$. The angle at $B$ is labelled $x^{\circ }$. The text "NOT TO SCALE" is shown to the right of the triangle.] The diagram shows...See it on the paper →
9. 0580/22 · February/March 2025 · Q14b(i)[2]
   A, B, C, D and E lie on a circle. FG is a tangential to the circle at C. Angle $BAD=110^{\circ }$, angle $ADB=20^{\circ }$ and angle $BEC=45^{\circ }$. [Diagram: A circle with points A, B, C, D, E on its circumference. Chords AB, BC, CD, DA, AC, BD, BE, CE are drawn. A tangent line FG touches the circle at C. Angle $BAD$...See it on the paper →
10. 0580/22 · February/March 2025 · Q14b(ii)[1]
    A, B, C, D and E lie on a circle. FG is a tangent to the circle at C. Angle $BAD=110^{\circ }$, angle $ADB=20^{\circ }$ and angle $BEC=45^{\circ }$. [Diagram: A circle with points A, B, C, D, E on its circumference. Chords AB, BC, CD, DA, AC, BD, BE, CE are drawn. A line FG is tangent to the circle at C. Angle $BAD$ is ma...See it on the paper →
11. 0580/32 · February/March 2025 · Q21a[1]
    21 (a) Show that the sum of the interior angles of a pentagon is $540^{\circ }$.See it on the paper →
12. 0580/32 · February/March 2025 · Q21b(i)[2]
    (b) In this part, all angles are in degrees. [Diagram: A pentagon with interior angles labelled $x+35$, $3x-25$, $3x-5$, $x+40$, and $2x$. The text "NOT TO SCALE" is written to the right of the shape.] The diagram shows the five interior angles of a pentagon, written in terms of $x$. (i) Write down an expression, in te...See it on the paper →
13. 0580/32 · February/March 2025 · Q21b(ii)[2]
    (b) In this part, all angles are in degrees. [Diagram: A pentagon with interior angles labeled $x+35$, $3x-25$, $3x-5$, $x+40$, and $2x$. The text "NOT TO SCALE" is written to the right of the shape.] The diagram shows the five interior angles of a pentagon, written in terms of $x$. (ii) Work out the value of $x.$See it on the paper →
14. 0580/13 · May/June 2024 · Q11[2]
    11 [Diagram: An isosceles triangle with the two equal sides marked with tick marks. The angle at the top vertex is labeled $x^{\circ }$. The angle at the bottom-left vertex is labeled $36^{\circ }$. The text "NOT TO SCALE" is to the right of the triangle.] The diagram shows an isosceles triangle. Find the value of $x$.See it on the paper →
15. 0580/11 · October/November 2023 · Q8[2]
    The diagram shows an isosceles triangle. [Diagram: An isosceles triangle with the two equal sides marked with tick marks. The angle at the top-left vertex is $41^{\circ }$. The angle at the bottom vertex is $x^{\circ }$. The text "NOT TO SCALE" is present.] Find the value of $x.$See it on the paper →
16. 0580/12 · May/June 2023 · Q5[2]
    [Diagram: A triangle $ABC$ with a straight line $ACD$ extending from $A$ through $C$ to $D$. Angle $BAC=73^{\circ }$, Angle $ABC=59^{\circ }$. Angle $BCA=x^{\circ }$ and Angle $BCD=y^{\circ }$. Labelled "NOT TO SCALE".] In the diagram, $ABC$ is a triangle and $ACD$ is a straight line. Find the value of $x$ and the value o...See it on the paper →
17. 0580/12 · May/June 2023 · Q17[2]
    17 Find the size of an interior angle of a regular 15-sided polygon.See it on the paper →
18. 0580/13 · May/June 2023 · Q12[2]
    Triangle $ABC$ is isosceles. Angle $BAC=38^{\circ }$ and $AB=AC$. [Diagram: Triangle $ABC$ with vertex $A$ at the top, $B$ at bottom left, $C$ at bottom right. Angle at $A$ is marked $38^{\circ }$. Angle at $B$ is marked $x^{\circ }$. Sides $AB$ and $AC$ have tick marks indicating they are equal. Text "NOT TO SCALE" is to...See it on the paper →
19. 0580/21 · May/June 2023 · Q1[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

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20. 0580/12 · February/March 2019 · Q6[1]

    1-mark “Explain” question — its maths and diagrams are best seen on the paper.

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What examiners said

Most candidates realised that angles BDC and BEC were in the same segment and therefore equal, and many went on to find angle DBC correctly. A small number incorrectly thought that angle ADC rather than angle BDC was equal to 45°.

— Examiner report, February/March 2025, 0580/22 Q14(b)(i) (Cambridge)

Most candidates used the alternate segment theorem correctly to find angle DCG, this was more often the correct answer but occasionally, a correct follow through from part (b)(i). The most common incorrect answer seen for this part was 45°.

— Examiner report, February/March 2025, 0580/22 Q14(b)(ii) (Cambridge)

This part was generally well answered with most using the (5 – 2) × 180 method. As this was a ‘show that’ question, full working is required and so answers such as 3 × 180 and 108 × 5 are deemed insufficient.

— Examiner report, February/March 2025, 0580/32 Q21(a) (Cambridge)