Question

Use the diagram below to answer the questions on the right:

(a) Find the value of y:
(b) Solve for x:
(c) Find the measure of (d) What is the measure of

Answer 1

y = 8

x = 18

m<F = 36°

m<D = 72°

Explanation:

Since angles D and E are congruent, then sides EF and DF are congruent.

EF = DF

2y + 5 = 21

2y = 16

y = 8

m<D + m<E + m<F = 180°

m<D = m<E = 4x°

4x + 4x + 2x = 180

10x = 180

x = 18

m<F = 2x°

m<F = 2 × 18°

m<F = 36°

m<D = 4x°

m<D = 4 × 18°

m<D = 72°