Find the measure of the following angle

Explanation

Note that ∠ABD and ∠CBE are vertical angles. By using this property you can find the values of x

m(∠ABD) = m(∠CBE)

2x +8 = 4x + 32^o ⇒

4x - 2x = 32^o - 8^o  ⇒

2x = 24^o ⇒

x = 12^o

 

then m(∠ABD) = 2 * 12^o + 8^o = 32^o

Since ∠ABD and ∠DBE are supplementary angles, then 

m(∠ABD) = 180^o - 32^o = 148^o