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Chapter 2: Q14. (page 46)

SW→bisects ∠RSTand m∠RST=72. SZ→bisects ∠RSW, and SR→bisects ∠NSW. Sketch a diagram and find m∠RSZandm∠RSZ

Short Answer

Expert verified

The diagram is:

And

m∠RSZ=18∘,m∠NSZ=54∘

Step by step solution

01

Step 1. Sketch the diagram.

SW→bisects ∠RSTand m∠RST=72. SZ→bisects ∠RSW, and SR→bisects ∠NSW.

Therefore, the diagram is:

02

Step 2. Calculate m∠RSZ.

Since SW→bisects ∠RST,

∠RSW=∠TSW=12∠RST∠RSW=∠TSW=12×72∘∠RSW=∠TSW=36∘

Now, it is known that SZ→bisects ∠RSW, so,

∠RSZ=∠WSZ=12∠RSW

Since ∠RSW=36∘, then,

∠RSZ=∠WSZ=12×36∘∠RSZ=∠WSZ=18∘∠RSZ=18∘

03

Step 3. Calculate m∠NSZ.

Again SR→bisects ∠NSWand ∠RSW=36∘, so,

∠NSR=∠RSW=12∠NSW∠NSR=∠RSW=36∘∠NSR=36∘

For ∠NSZ,

∠NSZ=∠NSR+∠RSZ∠NSZ=36∘+18∘=54∘

04

Step 4. State the conclusion.

Therefore, m∠RSZ=18∘ andm∠NSZ=54∘

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