Question

Please can somebody help me with these questions?

1. In the Circle Below, Quadrilateral WXYZ is inscribed in circle O. The m

Answer 1

(a) 107°

Explanation:

We can use the fact that opposite angles of a cyclic quadrilateral are supplementary to find the value of x. With that value, we can find the measure of angle W.

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∠X +∠Z = 180°

(5x +18)° +(3x +2)° = 180°

8x +20 = 180 . . . . . . . . . . . . divide by °, collect terms

8x = 160 . . . . . . . . . subtract 20

x = 20 . . . . . . divide by 8

Now, we can find the measure of ∠W:

∠W = (4x +27)° = (4·20 +27)° = (80 +27)°

∠W = 107°