We are given a triangle and an exterior angle formed by the support for a window air-conditioning unit. We are asked to find the measure of the exterior angle.
First, let's identify the exterior angle on the given diagram.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
We will now identify the two nonadjacent interior angles.
The nonadjacent interior angles are a right angle and 3x^(∘). We can write an equation to relate the exterior angle measure to the interior angles. Recall that the measure of a right angle is
90^(∘).
exterior angle measure= 3x^(∘)+ 90^(∘)
We need find the value of x to find this sum. We will do this using the rule for the interior angle measures of a triangle.
Interior Angle Measures of a Triangle
The sum of the interior angles of a triangle is 180^(∘).
By this rule, we can write the equation for the interior angles of the given triangle.
(5x-6)^(∘) + 3x^(∘)+ 90^(∘)=180^(∘)
Now, let's solve the equation for x.
We found that x= 12. We can substitute 12 for x to evaluate the expression for the exterior angle.
3x^(∘)+ 90^(∘) ⇒ 3( 12)^(∘)+90^(∘)
Let's simplify this expression!
