Exercise 34 Page 395

Let's consider the given diagram.

We see that we have three angles around point A. The sum of measures of angles around a point equals 360^(∘), so we can write the following equation for x. 140^(∘)+ (2x+4)^(∘) + (2x+6)^(∘) = 360^(∘) Let's solve it!

140^(∘)+(2x+4)^(∘) + (2x+6)^(∘) = 360^(∘)

AddTerms

Add terms

150^(∘) + 4x^(∘) = 360^(∘)

SubEqn

LHS-180^(∘)=RHS-180^(∘)

4x^(∘) = 210^(∘)

DivEqn

.LHS /4.=.RHS /4.

x^(∘) = 52.5^(∘)

Now, we can substitute x=52.5 into (2x+4)^(∘) and (2x+6)^(∘) to find the values of ∠ BAD and ∠ CAD.

Angle	x=52.5	Measure
∠ BAD=(2x+4)^(∘)	(2( 52.5)+4)^(∘)	109^(∘)
∠ CAD=(2x+6)^(∘)	(2( 52.5)+6)^(∘)	111^(∘)