A shaded isosceles triangle is drawn inside a rectangle. Calculate the size of angle 𝑎.
We know our shaded triangle is an isosceles triangle. Isosceles triangles have two sides which are equal in length. So we have two congruent sides or sides which are equal in length. And these two angles here are also congruent. This means we know two of the three angles.
We can use these two measurements to help us find the measurement of angle 𝑎. We know that these two angles measure 76 degrees in total because 38 times two is 76. We also need to know that angles on a straight line total 180 degrees. So if we take 76 degrees from 180 degrees, this will tell us the measurement of angle 𝑎. 180 subtract 76 is 104. So angle 𝑎 is 104 degrees.