Chapter 2: Q14. (page 46)

$\vec{S W}$ bisects $∠ R S T$ and $m ∠ R S T =72$ . $\vec{S Z}$ bisects $∠ R S W$ , and $\vec{S R}$ bisects $∠ N S W$ . Sketch a diagram and find $m ∠ R S Z$ and $m ∠ R S Z$

Short Answer

Expert verified

The diagram is:

And

$m ∠ R S Z = 18^{\circ}$ , $m ∠ N S Z = 54^{\circ}$

Step by step solution

Step 1. Sketch the diagram.

$\vec{S W}$ bisects $∠ R S T$ and $m ∠ R S T = 72$ . $\vec{S Z}$ bisects $∠ R S W$ , and $\vec{S R}$ bisects $∠ N S W$ .

Therefore, the diagram is:

Step 2. Calculate m∠RSZ.

Since $\vec{S W}$ bisects $∠ R S T$ ,

$∠ R S W = ∠ T S W = \frac{1}{2} ∠ R S T ∠ R S W = ∠ T S W = \frac{1}{2} \times 72^{\circ} ∠ R S W = ∠ T S W = 36^{\circ}$

Now, it is known that $\vec{S Z}$ bisects $∠ R S W$ , so,

$∠ R S Z = ∠ W S Z = \frac{1}{2} ∠ R S W$

Since $∠ R S W = 36^{\circ}$ , then,

$∠ R S Z = ∠ W S Z = \frac{1}{2} \times 36^{\circ} ∠ R S Z = ∠ W S Z = 18^{\circ} ∠ R S Z = 18^{\circ}$

Step 3. Calculate m∠NSZ.

Again $\vec{S R}$ bisects $∠ N S W$ and $∠ R S W = 36^{\circ}$ , so,

$∠ N S R = ∠ R S W = \frac{1}{2} ∠ N S W ∠ N S R = ∠ R S W = 36^{\circ} ∠ N S R = 36^{\circ}$

For $∠ N S Z$ ,

$∠ N S Z = ∠ N S R + ∠ R S Z ∠ N S Z = 36^{\circ} + 18^{\circ} = 54^{\circ}$

Step 4. State the conclusion.

Therefore, $m ∠ R S Z = 18^{\circ}$ and $m ∠ N S Z = 54^{\circ}$

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$\vec{S W}$ bisects $∠ R S T$ and $m ∠ R S T =72$ . $\vec{S Z}$ bisects $∠ R S W$ , and $\vec{S R}$ bisects $∠ N S W$ . Sketch a diagram and find $m ∠ R S Z$ and $m ∠ R S Z$

Short Answer

Step by step solution

Step 1. Sketch the diagram.

Step 2. Calculate m∠RSZ.

Step 3. Calculate m∠NSZ.

Step 4. State the conclusion.

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

Short Answer

Step by step solution

Step 1. Sketch the diagram.

Step 2. Calculate m∠RSZ.

Step 3. Calculate m∠NSZ.

Step 4. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

$\vec{S W}$ bisects $∠ R S T$ and $m ∠ R S T =72$ . $\vec{S Z}$ bisects $∠ R S W$ , and $\vec{S R}$ bisects $∠ N S W$ . Sketch a diagram and find $m ∠ R S Z$ and $m ∠ R S Z$