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

Answer:

m∠ABE = 27°

Step-by-step explanation:

In the attached figure, we see that m∠EBF = 117°

and BF is perpendicular to AC (BF is at a right angle to segment AC)

This leads to m∠ABF = m∠CBF = 90°

Now, from the relationship m∠EBF = m∠ABE + m∠ABF

                             117° = m∠ABE + 90°

So, m∠ABE = 117° - 90°

            = 27°

Consequently, the angle ABE measures 27°.

Answer:

m∠ABE = 27°

Step-by-step explanation:

* To analyze the figure to address the query

- AC represents a line

- Ray BF crosses line AC at point B

- Ray BF is perpendicular to line AC

Thus, both ∠ABF and ∠CBF are classified as right angles

Which gives us ∠ABF = ∠CBF = 90°

- Rays BE and BD meet line AC at point B

Since m∠ABE is equal to m∠DBE, as indicated by the same symbol in the figure

It implies that BE acts as the angle bisector of angle ABD

Given that m∠EBF = 117°

Then m∠EBF = m∠ABE + m∠ABF

Where m∠ABF = 90°

So, 117° = m∠ABE + 90°

- By subtracting 90 from both sides

It follows that m∠ABE = 27°