Question

Given: m∠V=103°, m∠VRT=71°, RS ∥ VU Find: m∠TRS, m∠U

Answer 1

m∠TRS = 6°

m∠U = 103°

Explanation:

In the given figure,

O is the center

RS ∥ VU

m∠V = 103° &

m∠VRT = 71°

So,

m∠V + m∠R = 180° (∵ sum of co-interior angles)

⇒ m∠R = 180° - 103° (m∠V = 103° is given)

∵ m∠R = 77° ...(i)

Now,

m∠R = m∠TRS + m∠VRT

by putting the values given

⇒ m∠TRS = 77° - 71°

∵ m∠TRS = 6°

As we know that,

VURT is a cyclic quadrilateral. So,

m∠U + m∠R = 180°

⇒ m∠U + 77° = 180° (from equation (i)

∵ m∠U = 180° - 77° = 103°