Question

can someone pls solve this for me

Answer 1

Given:

m∠WYX = 20°

m∠XYZ = 135°

To find:

The measure of arc WXZ.

Solution:

m∠WYZ = m∠WYX + m∠XYZ

m∠WYZ = 20° + 135°

m∠WYZ = 155°

The measure of inscribed angle is half of the intercepted arc.

$\Rightarrow m \angle WYZ = \frac{1}{2} m (ar WXZ)$

$\Rightarrow 155^\circ = \frac{1}{2} m (ar WXZ)$

Multiply by 2 on both sides.

$\Rightarrow 2\times 155^\circ = 2 \times \frac{1}{2} m (ar WXZ)$

$\Rightarrow 310^\circ = m (ar WXZ)$

The measure of arc WXZ IS 310°.