Exercise 65 Page 627

Let's start by finding the value of x. Then we will use it to calculate the value of y.

Value of x

In order to calculate the value of x, we need to analyze the given diagram. What is the relationship between the angles measuring 68^(∘) and 2x^(∘)?

Notice that these are corresponding angles. The Corresponding Angles Postulate tells us that if parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. Therefore, the angles measuring 68^(∘) and 2x^(∘) are congruent and their measures are equal. 68 = 2x We can solve this equation to find the value of x.

68 = 2x

RearrangeEqn

Rearrange equation

2x = 68

DivEqn

.LHS /2.=.RHS /2.

x= 34

Value of y

Before we find the value of y, we will first substitute the value of x into the expression (3x-15)^(∘) and calculate its value.

3x-15

Substitute

x= 34

3( 34)-15

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Evaluate

Multiply

Multiply

102-15

SubTerm

Subtract term

87

Let's mark on the diagram the measure we calculated above.

Now, to find the value of y, we can use the fact that the sum of the angles of a triangle is equal to 180^(∘). 68+87+y^2=180 Finally, we can solve the above equation to find the value of y.

68+87+y^2=180

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Solve for y

AddTerms

Add terms

155+y^2=180

SubEqn

LHS-155=RHS-155

y^2=25

SqrtEqn

sqrt(LHS)=sqrt(RHS)

y=± 5