Question

In the rectangle below, FH=4x+2, EG = 5x-8, and m
Find EI and m < EIH

Answer 1

21

108

Explanation:

The diagonals of a rectangle are congruent and bisect each other.

EG = FH

5x - 8 = 4x + 2

x = 10

EI = (1/2)EG

EI = (1/2)(5x - 8)

EI = (1/2)(42)

EI = 21

m<IGF = 36

m<IFG = m<IGH = 36

m<IFG + m<IGH + m<FIG = 180

36 + 36 + m<IGH = 180

m<IGH = 108

m<EIH = m<IGH (vertical angles)

m<EIH = 108