If m∠EJF = 115 and m∠JHF = 90, what is m∠KEJ?

Question

If m∠EJF = 115 and m∠JHF = 90, what is m∠KEJ?

Answer 1

The answer is 25°. The explanation is a bit involved.

1. Triangles KEJ and HFJ are at at least similar. You can show they have the same angles. Hence angle JKE is 90°
2. Angle EJF is given as 115°. Angle KJE forms a supplementary pair with angle EJF, so it is 180º - 115º = 65º.
3. You now have two of the three angles of triangle KEJ, one being 90º, the other 65º. That means the measure of angle KEJ = 180° - 90° - 65° = 25°.