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Chapter 1: Q. 34 WE (page 22)

AL鈫�bisects 鈭�KAT. Find the value ofx.

m鈭�2=x+12,m鈭�3=6x-20

Short Answer

Expert verified

The value ofx=22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=x+12,

Also鈭�SATis a straight angle therefore,role="math" localid="1649225335774" m鈭�1+m鈭�2+m鈭�3=180掳

03

- Calculate x.

In order to calculate the value of x, substitute x+12for m鈭�1, x+12for m鈭�2, 6x-2for m鈭�3into the equation m鈭�1+m鈭�2+m鈭�3=180掳 and simplify.

x+12+x+12+6x-20=180掳8x+4=180掳8x=176掳x=176掳8x=22掳

Therefore,x=22掳

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