CAIE IGCSE Mathematics Extended E4.6.1 Calculate Unknown Angles and Give Simple Explanations Using the Questions

Use angle sums at a point, on a straight line, in triangles and quadrilaterals, plus vertically opposite angles, to find unknown values and justify each step.

Exam points

Use angles around a point (360°), on a straight line (180°), and vertically opposite angles to calculate unknown angles.
Apply triangle (180°) and quadrilateral (360°) angle sums in single-step and multi-step problems.
Give the geometric reason for each calculation, and form a simple equation when unknown angles are expressed algebraically.

[Maximum number: 6]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

The diagram shows an isosceles triangle with the base extended.
Find the value of x.

[ 3 ]

111
M2 for $180-\frac{180-42}{2}$ oe or $42+\frac{180-42}{2}$ oe, or M1 for $\frac{180-42}{2}$ oe

(b)

The diagram shows three lines meeting at a point.

The ratio a: b: c=3: 4: 5.

Find the value of c.

Figure for Question (b) — CAIE IGCSE Mathematics Extended

NOT TO SCALE

[ 3 ]

150
M1 for $\frac{k}{3+4+5}\times p$ , where p=1,3,4 or 5, or $\frac5{12}$ oe
B1 for 360 used

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CAIE IGCSE Mathematics Extended E4.6.1 Calculate Unknown Angles and Give Simple Explanations Using the Questions question 1

Question (a)

Question (b)