Exercise 155 Page 447

Let's consider the given diagram.

We want to find the value of x. Let's start by noticing that the 10x+2^(∘) angle and the 128^(∘) angle form a straight angle. This means that the sum of their measures is 180^(∘). We can use this information to write an equation. (10x+2^(∘)) + 128^(∘) = 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.

(10x+2)+128=180

RemovePar

Remove parentheses

10x+2+128=180

AddTerms

Add terms

10x+130=180

SubEqn

LHS-130=RHS-130

10x=50

DivEqn

.LHS /10.=.RHS /10.

10x/10=50/10

SimpQuot

Simplify quotient

x=50/10

CalcQuot

Calculate quotient

x=5

We found that x=5^(∘).

We are given the following diagram.

To find the value of x, 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 our triangle. x+ 65^(∘)+ 80^(∘)=180^(∘) Let's solve the equation and find the value of x. We can ignore the degree symbol to make the math easier.

x+65+80=180

AddTerms

Add terms

x+145=180

SubEqn

LHS-145=RHS-145

x=35

We found that x=35^(∘).

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Exercise 155 Page 447

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