Question
Find MP in the given figure.
- 20
- 25
- 21
- 23
Hint:
Since, it is angular bisector. We can equalize the angle of two divisions and then obtain the measure of the required angle.
The correct answer is: 20
Angular Bisector:
In geometry, an angle bisector is a line that divides an angle into two equal angles. The term “bisector” refers to something that divides a form or object into two equal halves. An angle bisector is defined as a ray that divides an angle into two equal pieces of the same measure.
Given That:
*** From the angle bisector theorem,
MP = NP
5x + 15 = 12x + 8
12x – 5x = 15 – 8
7x = 7
x = 1
>>>> MP = 5 
1 + 15
= 5 + 15
= 20
>>>>Therefore, the measure of MP is 20.
Always angular bisector divides the given angle into 2 equal parts. Then, by equalizing the the two equations we can get the measure of angles easily.
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