Question

In the roof truss, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF.

Find the measure of each angle.
m∠DEF=
m∠ABG=
m∠CBG=
m∠DEG=

Answer 1

`m\angle CBG=56^(\circ)`

`m\angle ABG=56^(\circ)`

`m\angle DEG=56^(\circ)`

Explanation:

We have been given that ∠ABC≅∠DEF, so the measure of their corresponding will be equal.

Since line BG bisects ∠ABC and measure of angle ABC is 112 degrees, so measure of angle CBG and ABG will be half the measure of angle ABC.

`m\angle CBG=(1)/(2)m\angle ABC`

`m\angle CBG=(1)/(2)*112^(\circ)`

`m\angle CBG=56^(\circ)`

Therefore, measure of angle CBG and angle ABG will be 56 degrees.

We have been given that measure of angle DEF is equal to 112 degrees.

Since both triangles are congruent, so measure of angle DEG will be equal to measure of angle ABG.

Therefore, measure of angle DEG is 56 degrees.

Answer 2

In the given diagram, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF. So the measure of angles are :

1. m∠DEF= 112° because ∠ABC≅∠DEF

2. m∠ABG= 56° because a straight line BG is bisecting ∠ABC in two equal parts. So,
`(112)/(2) = 56`

3. m∠CBG= 56° because ∠ABG and ∠CBG are equal.

4. m∠DEG= 56° because ∠ABG ≅ ∠DEG