body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Angles of Triangles

Continue to next subchapter

Exercise 15 Page 339

Find the measure of ∠ 2 first.

m∠ 1=m∠ 2=59^(∘)
m∠ 3=99^(∘)

Practice makes perfect

Finding m∠ 2

In the right triangle △ LMN, the measure of one of the acute angles is given and we are asked to find the measure of the other acute angle.

According to Corollary 4.1 of the Triangle Angle-Sum Theorem the acute angles of a right triangle are complementary, so their measures add to 90^(∘).

m∠ 2+31=90

LHS-31=RHS-31

m∠ 2=59

The measure of ∠ 2 is 59^(∘).

Finding m∠ 1

Let's put the measure of ∠ 2 on the diagram and focus on the angles at point N. Angles ∠ 1 and ∠ 2 are vertical angles.

According to the Vertical Angles Theorem vertical angles are congruent, so they have the same measure. Since we now know the measure of ∠ 2, this tells us the measure of ∠ 1. m∠ 1=m∠ 2=59^(∘)

Finding m∠ 3

Let's put the measure of ∠ 1 on the diagram and switch our focus to triangle △ NPQ. In this triangle we now know the measure of two angles and are asked to find the measure of the third angle.

We can use the Triangle Angle-Sum Theorem in triangle △ NPQ to set up and solve an equation for m∠ 3.

m∠ N+m∠ P+m∠ Q=180

m∠ N= 59, m∠ P= 22

59+ 22+m∠ 3=180

▼

Solve for m∠ 3

Add terms

81+m∠ 3=180

LHS-81=RHS-81

m∠ 3=99

The measure of ∠ 3 is 99^(∘).

Subchapter links

Exercises p.339-343