Question

use the definition of an angle bisector to answer
each question below.

(d)16. if \\(\overline{yr}\\) bisects \\(\angle xyz\\) and \\(m\angle xyr = 48\\),
(12) then find \\(m\angle ryz\\).

1. if \\(\overline{bd}\\) bisects \\(\angle abc\\) and \\(m\angle abc = 32\\),

(12) then find \\(m\angle abd\\).

(e)18. if \\(\overline{ol}\\) bisects \\(\angle mop\\) and \\(m\angle mop = 74\\),
(12) then find \\(m\angle mol\\) and \\(m\angle lop\\).

Explanation:

Question 16

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal angles. So, if \(\overline{YR}\) bisects \(\angle XYZ\), then \(m\angle XYR = m\angle RYZ\).

Step2: Substitute given value

Given \(m\angle XYR = 48\), so \(m\angle RYZ = 48\).

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal angles. So, if \(\overline{BD}\) bisects \(\angle ABC\), then \(m\angle ABD=\frac{1}{2}m\angle ABC\).

Step2: Substitute given value

Given \(m\angle ABC = 32\), so \(m\angle ABD=\frac{32}{2}=16\).

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal angles. So, if \(\overline{OL}\) bisects \(\angle MOP\), then \(m\angle MOL = m\angle LOP=\frac{1}{2}m\angle MOP\).

Step2: Substitute given value

Given \(m\angle MOP = 74\), so \(m\angle MOL=\frac{74}{2}=37\) and \(m\angle LOP = 37\).

Answer:

\(48\)

Question 17