Question

How do I write down the size of the angles marked by letters by this trapezium, for this question?

Answer 1

In a trapezium, two adjacent angles, each one formed by one segment of a pair of opposite sides, supplementary. This means the measures of those two angles must sum up to 180º.

This is the case for pair a and 65º, and for pair b and 130º. Thus, we have:

a + 65º = 180º

and

b + 130º = 180º

Now, we can solve each of those equations by isolating the variable:

a + 65º = 180º

a + 65º - 65º = 180º - 65º

a = 115º

b + 130º = 180º

b + 130º - 130º = 180º - 130º

b = 50º

Therefore:

a = 115º

b = 50º