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

1 Answer
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 2x + 30 + 3x + 20 = 180 implies 5x + 50 = 180#
#implies 5x = 180 - 50#
#implies x = 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 2x + 30 = 3x + 20#
#implies 30 - 20 = 3x - 2x#
#implies x = 10#
Thus both angles are 50 degrees.