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Chapter 5: Q11 (page 187)

Quad. is a rhombus.

If m∠1=25, find the measures of ∠2,∠3,∠4and∠5.

Short Answer

Expert verified

The measures of ∠2,∠3,∠4and∠5are 25°,65°,65°and90°respectively.

Step by step solution

01

Step 1. Property of rhombus.

The diagonals of a rhombus are perpendicular.

In quad. SLTM, LM and ST are diagonals of rhombus then by property of rhombus, m∠5=90°.

02

Step 2. Description of step.

Diagonals of a rhombus bisects the vertex angles.

Here, ∠LSMis divided into ∠1and∠2, that is, m∠1=m∠2. As m∠1=25, m∠2=25°.

03

Step 3. Description of step.

Here, ∠SLTis divided into ∠3and∠4, that is, m∠3=m∠4.

04

Step 4. Description of step.

Here, ∠Sand∠L are supplementary.

Substitute m∠3for m∠4.

m∠1+m∠2+m∠3+m∠4=18025+25+m∠3+m∠3=1802m∠3=180−502m∠3=130m∠3=65°

05

Step 5. Description of step.

As m∠3=65°and m∠3=m∠4implies that m∠4=65°.

Therefore, the measures of ∠2,∠3,∠4and∠5are 25°,65°,65°and90°respectively.

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