Questions: Select the correct answer. In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H ? A. 42° B. 45° C. 48° D. 93°

Solution Steps

We are given that angle D measures 45° and angle E measures 87°.

The figure is a square with diagonals intersecting at point E. In a square, all internal angles are 90°. The diagonals of a square bisect each other at right angles (90°).

Since angle D is 45° and it is part of a right triangle (formed by the diagonal), the other angle in the triangle (angle F) must be 45° because the sum of angles in a triangle is 180°.

Angle H is part of the right triangle formed by the diagonal and the side of the square. Since angle E is 87° and angle F is 45°, angle H can be found by subtracting the sum of angles E and F from 180°: \[ \text{Angle H} = 180° - 87° - 45° = 48° \]

Final Answer