Exercise 16 Page 379

m∠ SRT=65

Practice makes perfect

Looking at the markings on the given figure, we can see that ST≅ RT.

To find m ∠ SRT, we will consider the Isosceles Triangle Theorem

Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Using this theorem, let's show the congruent angles and label them as x^(∘).

Now, we can find m ∠ SRT using the Triangle Angle-Sum Theorem.

m ∠ RST+m ∠ SRT+m ∠ RTS=180

Substitute values

x+x+50=180

Add terms

2x+50=180

LHS-50=RHS-50

2x=130

.LHS /2.=.RHS /2.

x=65

We found that the value of x is 65, so the measure of ∠ SRT is 65^(∘).

Exercises p.378-382

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