Exercise 30 Page 177

We want to find value of the variable x and the measures of the angles for the given triangle.

To do this, we will use the Triangle Angle-Sum Theorem. This theorem tells us that the measures of the interior angles of a triangle must add to 180^(∘).

Applying the theorem, we can create an equation by adding the given expressions and setting the sum equal to 180. Notice that m ∠ B = 90, because this angle is marked with a square angle marker. ( 4x+7)+ 90+( 8x-1)=180 Let's solve the equation for x.

( 4x+7)+ 90+( 8x-1)=180

RemovePar

Remove parentheses

4x+7+90+8x-1=180

AddSubTerms

Add and subtract terms

12x+96=180

SubEqn

LHS-96=RHS-96

12x=84

DivEqn

.LHS /12.=.RHS /12.

x= 7

Now that we know the value of x, we can substitute this into the given expressions to find the angle measures of △ ABC. m∠ A &= 4x+7 ⇒ &4( 7)+7&=35 m∠ C &= 8x-1 ⇒ &8( 7)-1&=55