Question

Find the value of x in each case:(Will give brainliest)

Answer 1

Answer:

x= 22.5°

Step-by-step explanation:

∠DEA= ∠BAE (alt. ∠s, DE// AB)

Substitute ∠DEA= 2x:

∠BAE= 2x

∠AEB +∠BEF= 180° (adj. ∠s on a str. line)

Substitute ∠BEF= 4x:

∠AEB +4x= 180°

∠AEB= 180° -4x

∠ABE +∠CBE= 180° (adj. ∠s on a str. line)

Substitute ∠CBE= 6x:

∠ABE +6x= 180°

∠ABE= 180° -6x

∠BAE +∠AEB +∠ABE= 180° (∠ sum of triangle)

2x +180° -4x +180° -6x= 180°

-8x +360°= 180°

8x= 360° -180°

8x= 180°

x= 180° ÷8

x= 22.5°