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Chapter 4: Q7. WE (page 137)

Find the value of x.

Short Answer

Expert verified

The value ofx is 41掳.

Step by step solution

01

Step 1. Name the given figure and highlight ∠x.

02

Step 2. Description of step.

Consider 螖ABDand 螖BCD, from the given figure it can be observed that, AD炉鈮�CD炉,AB炉鈮�CB炉and BD炉is common side to both the triangles. Therefore, by SAS postulate,

m鈭�A=m鈭�C=98

03

Step 3. Description of step.

Consider螖BCD in whichCD炉鈮�CB炉 it implies that螖BCD is an isosceles triangle.

Therefore,

鈭�CBD鈮�鈭�BDC鈭�CBD=x

04

Step 4. Apply an angle sum theorem.

Consider螖BCD such that,

m鈭�CBD+m鈭�BCD+m鈭�BDC=180x+98+x=1802x+98=1802x=82x=41

Therefore, the value of xis 41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.

Write proof in two-column form.

Given: AD炉鈯�BC炉; BA炉鈯�AC炉.

Prove: 鈭�1鈮�鈭�2.

Suppose you know that DB炉鈯�DC炉.Explain how you can deduce that DB炉鈯�BA炉.

Plot the given points on graph paper. Draw 螖ABCand 螖DEF. Copy and complete the statement 螖ABC鈮�?炉.

A鈭�3,1B2,1C2,3

D4,3E(6,3)F6,8

State whether the congruence of triangles have the reflexive property, the symmetric property, the transitive property.
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