Exercise 34 Page 406

Practice makes perfect

Let's consider the given diagram.

We want to find the value of x. Let's start by noticing that the 132^(∘) angle and the 2x+3^(∘) angle form a straight angle. This means that the angles are supplementary and the sum of their measures is 180^(∘). We can use this information to write an equation. 132^(∘) + (2x+3^(∘)) = 180^(∘) Now we can solve this equation for x using the Properties of Equality. Let's ignore the degree symbol to make the math easier.

132+(2x+3)=180

RemovePar

Remove parentheses

132+2x+3=180

AddTerms

Add terms

135+2x=180

SubEqn

LHS-135=RHS-135

2x=45

DivEqn

.LHS /2.=.RHS /2.

2x/2=45/2

SimpQuot

Simplify quotient

x=45/2

CalcQuot

Calculate quotient

x=22.5

We found that x=22.5^(∘).

We are given the following diagram.

We are asked to find the values of d and e. Let's start with d. Notice that the 131^(∘) angle and angle d form a straight angle, which means that the angles are supplementary and the sum of their measures is 180^(∘). With this in mind, let's write an equation. 131^(∘) + d = 180^(∘)Now we can solve this equation for d. Again, let's ignore the degree symbol to make the math easier.

131+d=180

SubEqn

LHS-131=RHS-131

d=49

We found that d= 49^(∘).

To find the value of e, let's first recall a key piece of information about triangles.

Angle Sum Theorem for Triangles
The sum of the measures of the interior angles of a triangle is 180^(∘).

With this rule, we can write an equation connecting the measures of the angles of the triangle. 49^(∘)+ e+ 90^(∘)=180^(∘) Let's solve the equation and find the value of e.

49+e+90=180

AddTerms

Add terms

139+e=180

SubEqn

LHS-139=RHS-139

e=41

We found that e= 41^(∘).

Let's consider the given diagram.

We want to find the value of t. Let's recall another key piece of information about triangles.

Exterior Angle Theorem for Triangles
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Notice that angle t is an exterior angle and its remote interior angles are 19^(∘) and 24^(∘). With this in mind, we can write an equation using the Exterior Angle Theorem for Triangles. t= 19^(∘)+ 24^(∘) Now, we can solve this equation for t.

t=19+24

AddTerms

Add terms

t=43

We found that t= 43^(∘).

Subchapter links

9.1.1 Parallel Line Angle Pair Relationships p.397-398

9.1.2 Finding Unknown Angles in Triangles p.402

9.1.3 Exterior Angles in Triangles p.405-406

9.1.4 AA Triangle Similarity p.409-410

Exercise 34 Page 406

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