Question

Find the value of the lettered angles in each of the following ( see image ).

Please show workings.

The only given angles are 60° , 10° , 40°​

Answer 1

Explanation:

s + 40 + 60 = 180 {angle sum property}

s + 100 = 180

s = 180 - 100

s = 80

This figure is a cyclic quadrilateral. sum of opposite angles are 180

s + v + 60 + 10 = 180

80 + v + 60 + 10 = 180

v + 150 = 180

v = 180 - 150

v = 30

y+ 10 + v = 180 {angle sum property}

y + 10 + 30 = 180

y + 40 = 180

y = 180 - 40

y = 140

Answer 2

9514 1404 393

Answer:

r = 80°, s = 80°, t = 10°, u = 60°, v = 30°

Explanation:

Working clockwise from the left side, we can name the points on the circle as A, B, C, D. The given inscribed angles are half the measure of the arcs they intercept, so we have ...

arc BD = 2×40° = 80°

arc DA = 2×60° = 120°

arc CD = 2×10° = 20°

From these measures, we can deduce the measures of the individual arcs as ...

arc AB = 360° -BD -DA = 360° -80° -120° = 160°

arc BC = BD -CD = 80° -20° = 60°

Then the angle measures of interest are ...

r = AB/2 = 80°

s = AB/2 = 80°

t = CD/2 = 10°

u = DA/2 = 60°

v = BC/2 = 30°