Question

Triangle abc is congruent to triangle def. angle b is a right angle, and m∠c = 57°. what is m∠d? (1 point) 33° 43° 52° 57°

Answer 1

To find the measure of angle D in congruent triangles ABC and DEF, we use the fact that the sum of angles in a triangle is 180°. Since angle B is 90° and angle C is 57°, angle A and thus angle D must be 33°.

Step-by-step explanation:

The question is asking for the measure of angle D in two congruent triangles, where angle B is a right angle and angle C measures 57°. From the property that the sum of the angles in a triangle is always 180°, we can calculate the missing angle in triangle ABC, which will have the same measure as angle D in triangle DEF due to their congruency.

Let's calculate it step by step:

1. Angle B is a right angle, so it measures 90°.
2. Angle C is given as 57°.
3. The sum of angles in a triangle is 180°, so m∠A = 180° - (90° + 57°) = 180° - 147° = 33°.
4. Since triangles ABC and DEF are congruent, m∠D = m∠A = 33°.

Answer 2

The measure of angle D in a pair of congruent triangles where angle B is a right angle and angle C is 57° is 33°, since corresponding angles of congruent triangles are equal and the sum of the angles in a triangle is 180°.

Step-by-step explanation:

The question asks us to find the measure of angle D in a pair of congruent triangles, where triangle ABC is congruent to triangle DEF, angle B is a right angle, and the measure of angle C is 57°. Since the triangles are congruent, corresponding angles are equal. We know that the sum of the angles in any triangle is always 180°. As we have a right angle in both triangles (angle B and angle E), we know that both are 90°. Therefore, we can calculate the measure of angle A by subtracting the measures of angles B and C from 180°: 180° - 90° - 57° = 33°. This means that the measure of angle A is 33°. Given that triangle ABC is congruent to triangle DEF, angle D corresponds to angle A, therefore the measure of angle D is also 33°.