Question

In trapezium Efgh with eh parallel to fg, fe and gh are produced to meet at j. Given that angle ehf = 62 deg, angle efh = 25 deg, and angle jgf = 77 deg, what is the measure of angle ejh?

Answer 1

The measure of angle ejh in trapezium Efgh, where eh is parallel to fg and fe and gh meet at j, is 93 degrees.

Step-by-step explanation:

The question asks for the measure of angle ejh in a trapezium Efgh. To find this angle, we will use the given angles and the properties of a trapezium and the angles of a triangle. Given that angle ehf = 62°, angle efh = 25°, and angle jgf = 77°, the measure of angle ejh can be calculated as follows:

Since eh is parallel to fg and fe and gh are produced to meet at j, angle ehj and angle jgf form a linear pair and are supplementary, meaning they add up to 180°. Therefore, angle ehj = 180° - 77° = 103°.

Now, let's calculate the measure of angle ejh within triangle efh using the sum of angles in a triangle, which is 180°. Since the angles of triangle efh are angle ehf, angle efh, and angle ejh, we have 62° + 25° + angle ejh = 180°. Solving for angle ejh, we get angle ejh = 180° - 62° - 25° = 93°.