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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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Most popular questions from this chapter

a. Complete.

b. Study the pattern in the four cases shown, and predict the number of angles formed by six noncollinear rays that have the same endpoint.

c. Which of the expression below gives the number of angles formed by noncollinear rays that have the same endpoint?

n-12n-3n2-3localid="1649226517529" n(n-1)2

Make a sketch showing four coplanar points such that three, but not four, of them, are collinear.

If you measure 鈭�EFGwith a protractor you get more than 90掳. But you know that 鈭�EFGrepresents a right angle in a box. Using this as an example, complete the table.

Name three lines that intersect at point E.

Study a corner of your classroom where two walls and the ceiling meet. How many right angles can you see at the corner?
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