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.

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