Question

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

Answer 1

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.