Chapter 8: Q1. (page 287)

Use the diagram to complete each statement..
$\begin{array}{l} I f m ∠ R = 30, t h e n m ∠ R S U = ?, \\ m ∠ T S U = ?, a n d m ∠ T = ? \end{array}$

Short Answer

Expert verified

The measure of angles,

$\begin{array}{l} m ∠ R S U = 60^{\circ} \\ m ∠ T S U = 30^{\circ} \\ m ∠ T = 60^{\circ} \end{array}$ .

Step by step solution

Step 1. Given information.

Figure is given.

$m ∠ R = 30 °$

Step 2. Concept used.

Sum of the internal angles in a triangle is $180^{\circ}$

Step 3. Now find radii.

In triangle RSU,

$\begin{matrix} m ∠ R + m ∠ R S U + m ∠ R U S = 180^{\circ} \\ 30^{\circ} + m ∠ R S U + 90^{\circ} = 180^{\circ} \\ m ∠ R S U + 120^{\circ} = 180^{\circ} \\ m ∠ R S U = 60^{\circ} \end{matrix}$

Now

$\begin{matrix} m ∠ R S U + m ∠ T S U = 90^{\circ} \\ 60^{\circ} + m ∠ T S U = 90^{\circ} \\ m ∠ T S U = 30^{\circ} \end{matrix}$

In triangle STU,

$\begin{matrix} m ∠ S U T + m ∠ T S U + m ∠ T = 180^{\circ} \\ 90^{\circ} + 30^{\circ} + m ∠ T = 180^{\circ} \\ 120^{\circ} + m ∠ T = 180^{\circ} \\ m ∠ T = 60^{\circ} \end{matrix}$

Therefore, the measure of $m ∠ R S U = 60 °, m ∠ T S U = 60 °, m ∠ T = 60 °$ .

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Use the diagram to complete each statement..
$\begin{array}{l} I f m ∠ R = 30, t h e n m ∠ R S U = ?, \\ m ∠ T S U = ?, a n d m ∠ T = ? \end{array}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Now find radii.

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Use the diagram to complete each statement..Ifm∠R=30,thenm∠RSU=?,m∠TSU=?,andm∠T=?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Now find radii.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Decision Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use the diagram to complete each statement..
$\begin{array}{l} I f m ∠ R = 30, t h e n m ∠ R S U = ?, \\ m ∠ T S U = ?, a n d m ∠ T = ? \end{array}$