Question

What is Question I (if m<EBF = 117°, fine m<ABE)​

Answer 1

m∠ABE = 27°

Explanation:

In the figure attached, It is given that m∠EBF = 117°

and BF ⊥ AC (BF is perpendicular to segment AC)

Therefore, m∠ABF = m∠CBF = 90°

Now we know m∠EBF = m∠ABE + m∠ABF

117° = m∠ABE + 90°

m∠ABE = 117° - 90°

= 27°

Therefore, measure of angle ABE is 27°.

Answer 2

m∠ABE = 27°

Explanation:

* Lets look to the figure to solve the problem

- AC is a line

- Ray BF intersects the line AC at B

- Ray BF ⊥ line AC

∴ ∠ABF and ∠CBF are right angles

∴ m∠ABF = m∠CBF = 90°

- Rays BE and BD intersect the line AC at B

∵ m∠ABE = m∠DBE ⇒ have same symbol on the figure

∴ BE is the bisector of angle ABD

∵ m∠EBF = 117°

∵ m∠EBF = m∠ABE + m∠ABF

∵ m∠ABF = 90°

∴ 117° = m∠ABE + 90°

- Subtract 90 from both sides

∴ m∠ABE = 27°