Exercise 4 Page 646

Consider the Triangle Angle-Sum Theorem.

42^(∘), 48^(∘)

Practice makes perfect

Let's analyze the given triangle.

According to the Triangle Angle-Sum Theorem the measures of the interior angles of a triangle add to 180^(∘). Since one of the angles is a right angle, the acute angles are complementary. In this case, it means that 8x and 7x add to 90. 8x+7x=90 We will now solve the above equation for x.

8x+7x=90

AddTerms

Add terms

15x=90

DivEqn

.LHS /15.=.RHS /15.

x=6

Once we know the value of x, we can find the measures of acute angles. ccc 8x^(∘) &→& 8( 6)^(∘)&→& 48^(∘) 7x^(∘) &→& 7( 6)^(∘)&→& 42^(∘) Therefore, the measures of the acute angles are 42^(∘) and 48^(∘).

Subchapter links

1 Angles of Triangles p.646

2 Congruent Polygons p.646

3 Proving Triangle Congruence by SAS p.647

4 Equilateral and Isosceles Triangles p.647

5 Proving Triangle Congruence by SSS p.648

6 Proving Triangle Congruence by ASA and AAS p.649

7 Using Congruent Triangles p.649

8 Coordinate Proofs p.650

Exercise 4 Page 646

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