Question

use the figure and the given hypothesis to draw a conclusion and explain why with a theorem, postulate or definition.

1. if ∠abe is a right - angle. then it is 90°. why: def of right angle
2. if ∠1 and ∠5 are vertical angles. then ∠1≅∠5. why: def of vertical ∠s
3. if (overline{bf}) bisects ∠ebc. why: def of angle bisect
4. if d is in the interior of ∠abg. why: the angle addition postulate.
5. if ∠dba and ∠abf are supplementary angles. why: def of supplementary
6. if ∠1 is the complement to ∠2. why: def of complementary

use what you know about linear pairs of angles and vertical angles to calculate the measure of each lettered angle.
(a = 61^{circ})
(c = 52^{circ})
(119^{circ})

Explanation:

13.

Step1: Recall right - angle definition

A right angle is defined as an angle with a measure of 90°.

Step1: Recall vertical - angle property

Vertical angles are congruent by the definition of vertical angles.

Step1: Apply angle - bisector definition

If a ray bisects an angle, it divides the angle into two congruent angles. So, $\angle EBF\cong\angle FBC$.

Answer:

$m\angle ABE = 90^{\circ}$

14.