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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
1. Angles of Triangles
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Exercise 23 Page 340

Use the relationship between the acute angles of a right triangle.

78^(∘)

Practice makes perfect

We are given the measure of one of the acute angles of a right triangle and are asked to find the measure of the other acute angle. Let's introduce the variable x^(∘) for the unknown measure.

According to Corollary 4.1 of the Triangle Angle-Sum Theorem, the acute angles of a right triangle are complementary, so their measures add up to 90^(∘). x^(∘)+12^(∘)=90^(∘) Now, we will solve this equation for x.
x^(∘)+12^(∘)=90^(∘)
SubEqn

LHS-12^(∘)=RHS-12^(∘)

x^(∘)=78^(∘)
The measure of the angle the ramp makes with the van door is 78^(∘).

Extra

 Pair of Angles

Pairs of angles can be classified in different ways depending on how their measures relate. Let's see this classification in the following table!

Pair of Angles
Complementary Angles Two angles whose measures add up to 90^(∘) or π2 radians.
Supplementary Angles Two angles whose measures add up to 180^(∘) or π radians. They are also called linear pair because they form a straight angle.
Vertical Angles Vertical angles are formed on opposite sides of the point of intersection.
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