Question

Quadrilateral TUVW is inscribed in the circle. Find m∠T, m∠U, m∠V, m∠W.

Answer 1

m∠T = 68°

m∠U = 95°

m∠V = 112°

m∠W = 85°

Explanation:

m<V = (14z - 7)°

m<W = 10z°

m<T = 8z°

Recall that the sum of the opposite angles of a cyclic quadrilateral equals 180°.

Therefore:

(14z - 7)° + 8z° = 180°

Find z

14z - 7 + 8z = 180

22z - 7 = 180

22z = 180 + 7

22z = 187

22z/22 = 187/22

z = 8.5

Plug in the value of z in each case

✅m<V = (14z - 7)° = 14*8.5 - 7 = 112°

✅m<W = 10z° = 10*8.5 = 85°

✅m<T = 8z° = 8*8.5 = 68°

✅m<U = 180 - m<W

m<U = 180 - 85 = 95°