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Chapter 1: Q33. (page 22)

AL鈫�bisects 鈭�KAT. Find the value of x.

m鈭�1=2x-8,m鈭�3=116

Short Answer

Expert verified

The value of x=20掳.

Step by step solution

01

- Line bisector and straight angle

If a line bisects angles, it divides it into two equal parts.

Measure of straight angle is 180掳.

02

- Observe the figure

The given figure is

From the figure, since AL鈫�bisects 鈭�KAT, therefore, m鈭�1=m鈭�2=2x-8.

Also 鈭�SATis a straight angle therefore,

m鈭�1+m鈭�2+m鈭�3=180掳

03

- Calculate x.

In order to calculate the value of x, substitute 2x-8for m鈭�1, 2x-8for m鈭�2, 116 for m鈭�3into the equation m鈭�1+m鈭�2+m鈭�3=180掳and simplify.

role="math" localid="1649246369856" 2x-8+2x-8+116=180掳4x-16=180掳-1164x=80x=20掳

Therefore,x=20掳

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