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Chapter 4: Q8. WE (page 137)

Find the value of x.

Short Answer

Expert verified

The value ofx is 30掳.

Step by step solution

01

Step 1. Name the given figure.

02

Step 2. Description of step.

Consider螖ABC from the given figure it can be observed that, AB炉鈮�AC炉. It implies that螖ABC is an isosceles triangle. Therefore,

鈭�ABC鈮�鈭�ACB

03

Step 3. Description of step.

If two lines are intersected by transversal then the angle formed by transversal with respect to two lines are equal.

Here,DE炉||BC炉 which implies that鈭�ABC=鈭�BAD and 鈭�ACB=鈭�CAE.

Therefore, 鈭�BAD=鈭�CAE.

04

Step 4. Description of step.

Substitute 2xfor 鈭�BADand 90鈭�xfor 鈭�CAEinto the equation obtained in step 3.

2x=90鈭�x3x=90x=30

Therefore, the value of xis 30掳.

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Plot the given points on graph paper. Draw 螖ABCand DE炉. Find two locations of point Fsuch that 螖ABC鈮�螖DEF.

A鈭�1,0B鈭�5,4C鈭�6,1D1,0E5,4.

Is the following statement 鈥淐orresponding parts of congruent triangles are congruent鈥� based on a definition, postulate, or theorem?

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

In the following figure, the two-triangle shown are congruent. Then complete the following statement.

BO=___
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