Describing Triangles

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

The interior angles theorem tells us that the measures of the interior angles of a triangle must add to

18 0^{\circ} .

Applying the theorem, we can create an equation by adding the given expressions and equating the sum to

180 .

We notice that one of the angles is a right angle, and therefore its measure is

90 .

(2 x + 4) + (5 x - 5) + 90 = 180

Let's solve the equation for

x .

(2 x + 4) + (5 x - 5) + 90 = 180

RemoveParRemove parentheses

2 x + 4 + 5 x - 5 + 90 = 180

AddSubTermsAdd and subtract terms

7 x + 89 = 180

LHS - 89 = RHS - 89

7 x = 91

LHS / 7 = RHS / 7

x = 13

Now that we know the value of

x,

we can substitute

x = 13

into the given expressions to find the angle measures of the triangle.

2 x + 4 \Rightarrow 5 x - 5 \Rightarrow 2 (13) + 4 5 (13) - 5 = 30 = 60

Describing Triangles 1.12 - Solution