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Chapter 8: Q1. (page 287)

Use the diagram to complete each statement..

Ifm∠R=30,thenm∠RSU=?,m∠TSU=?,andm∠T=?

Short Answer

Expert verified

The measure of angles,

m∠RSU=60∘m∠TSU=30∘m∠T=60∘.

Step by step solution

01

Step 1. Given information.    

Figure is given.

m∠ R=30°

02

Step 2. Concept used.

Sum of the internal angles in a triangle is 180∘

03

Step 3. Now find radii.

In triangle RSU,

m∠ â¶Ä‹R+m∠​RSU+m∠​RUS=180∘30∘+m∠​RSU+90∘=180∘m∠​RSU+120∘=180∘m∠​RSU=60∘

Now

m∠​â¶Ä‰RSU+m∠​â¶Ä‰TSU=90∘60∘+m∠​â¶Ä‰TSU=90∘m∠​â¶Ä‰TSU=30∘

In triangle STU,

m∠​â¶Ä‰SUT+m∠​â¶Ä‰TSU+m∠ â¶Ä‹T=180∘90∘+30∘+m∠ â¶Ä‹T=180∘120∘+m∠ â¶Ä‹T=180∘m∠ â¶Ä‹T=60∘

Therefore, the measure of m∠RSU=60°,m∠TSU=60°,m∠T=60°.

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Most popular questions from this chapter

Use the diagram to complete each statement.

If m∠R=k, then m∠RSU=?,

m∠TSU=?, and m∠T=?.

Find the values of x,y,and z.

Find the values of x,y,and z.

Find the value of x from the given figure.

Simplify.

45
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