# Angles (2(x+15)) and (3x+20) are a pair of interior angles. What are their values?

May 1, 2018

If you mean they are co-interior the angles are 82 and 98 degrees respectively.

If you mean they are alternate interior angles the angles are both 50 degrees.

#### Explanation:

I assume you mean the (co)interior angles made by a transversal on either side of a pair of parallel lines. In that case, $x = 26$ and the angles are 82 deg. and 98 deg. respectively.
This is because the sum of co-interior angles adds up to 180 degrees(they are supplementary).

$\implies 2 x + 30 + 3 x + 20 = 180 \implies 5 x + 50 = 180$
$\implies 5 x = 180 - 50$
$\implies x = \frac{130}{5} = 26$
Substitute $x = 26$ to get 82 and 98 as the angles.

Else if you mean alternate interior angles then $x = 10$ and the angles are both 50 degrees. In this case, both angles must be equal. This is a property of parallel lines(alt. int. angles are of the same measure).
$\implies 2 x + 30 = 3 x + 20$
$\implies 30 - 20 = 3 x - 2 x$
$\implies x = 10$
Thus both angles are 50 degrees.