Question

In the figure, BP is an angle bisector of ∠CBD. Find x if m∠1 = 4x - 8 and m∠2 = 3x + 2.

A) 5

B) 7

C) 9

D) 10

I am spacing out the words of the link for the picture, so just put the symbols/letters into place. https://www. usatestprep.com /modules/questions /files /image/ 451840.j pg

Answer 1

Answer:

Option D) 10

Therefore the value of x is 10.

Step-by-step explanation:

Given:

BP is an angle bisector of ∠CBD.

m∠1 = 4x - 8 and

m∠2 = 3x + 2.

To Find:

x = ?

Solution:

Angle Bisector:

A line that splits an angle into two equal angles.

Bisect means to divide into two equal parts.

Here, BP is an angle bisector of ∠CBD.

∴ m∠ 1 = m∠ 2

Substituting the given values we get

$(4x-8)=(3x+2)\\\\4x-3x=8+2\\\\x=10\\\\\therefore x = 10$

Therefore the value of x is 10.