Question

Find the value of each variable in each parallelogram

F 2y
G (x - 5)°
H (2x + 11)
D

Answer 1

Explanation:

Consecutive angles of a parallelogram equal 180°.

Opposite angles are congruent,

Using this set ∠G and ∠H equal to 180° and solve for x.

(x - 5) + (2x + 11) = 180°

x - 5 + 2x + 11 = 180°

3x + 6 = 180

3x + 6 - 6 = 180 - 6

3x = 174

3x/3 = 174/3

x = 58

∠G = x - 5

∠G = 58 -5

∠G = 53 °

Since opposite angles are congruent

∠D is also 53°

∠H = 2x + 11

∠H = 2(58) + 11

∠H = 116 + 11

∠H = 127°

opposite angles being congruent

∠F = 127°

so

127 = 2y

127/2 = 2y/2

y = 63.5°