Calculate the size of angles 𝑎 and 𝑏 in this diagram.
We need to calculate the size of these two angles, 𝑎 and 𝑏. This shape is a quadrilateral; it has four sides. The angles in a quadrilateral add up to 360 degrees. This angle is a right angle. So we know it measures 90 degrees. So this angle also measures 90 degrees. Angle 𝑎 is equal to its opposite angle, which is 160 degrees.
Now, we just need to calculate how much angle 𝑏 measures. We already have the measurements for the other three angles, 90 plus 90 plus 160. 90 and 90 is 180. 180 add 160 is 340. We know that the angles in a quadrilateral total 360 degrees. So we can subtract the sum of the other three angles from 360. 360 subtract 340 equals 20. So angle 𝑏 measures 20 degrees. Angle 𝑎 is 160 degrees and angle 𝑏 is 20 degrees.