Exercise 30 Page 341

We want to find the value of 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. 2x+ 3x+ 4x=180 Let's solve the equation for x.

2x+3x+4x=180

AddTerms

Add terms

9x=180

DivEqn

.LHS /9.=.RHS /9.

x=20

Now that we know the value of x, we can substitute x=20 into the given expressions to find the angle measures of the triangle. 2x ⇒ &2(20)&=40 3x ⇒ &3(20)&=60 4x ⇒ &4(20)&=80