Exercise 27 Page 520

Angles formed above and below a horizontal line have specific names. The angle formed above a horizontal line is called an angle of elevation. The angle formed below a horizontal line is called an angle of depression.

Notice that these two angles are congruent because they are alternate interior angles. Therefore, their measures are equal. 3(x+3)= (x+21) Let's solve our equation for x!

3(x+3)=(x+21)

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Solve for x

Distr

Distribute 3

3x+9=(x+21)

RemovePar

Remove parentheses

3x+9=x+21

SubEqn

LHS-x=RHS-x

2x+9=21

SubEqn

LHS-9=RHS-9

2x=12

DivEqn

.LHS /2.=.RHS /2.

x=6

Now that we found x, we will substitute its value into the given expressions to find the measure of each angle.

	Expression	Substitute	Value
Angle of Elevation e	(x+21)^(∘)	( 6+21)^(∘)	27^(∘)
Angle of Depression d	3(x+3)^(∘)	3( 6+3)^(∘)	27^(∘)