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Chapter 4: Q7. WE (page 137)

Find the value of x.

Short Answer

Expert verified

The value ofx is 41°.

Step by step solution

01

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

02

Step 2. Description of step.

Consider ΔABDand ΔBCD, from the given figure it can be observed that, AD¯≅CD¯,AB¯≅CB¯and BD¯is common side to both the triangles. Therefore, by SAS postulate,

m∠A=m∠C=98

03

Step 3. Description of step.

ConsiderΔBCD in whichCD¯≅CB¯ it implies thatΔBCD is an isosceles triangle.

Therefore,

∠CBD≅∠BDC∠CBD=x

04

Step 4. Apply an angle sum theorem.

ConsiderΔBCD such that,

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

Therefore, the value of xis 41°.

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

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