If triangle A B C is congruent to triangle D E F, the measure of angle A equals 55 degrees, and the measure of angle E equals 25 degrees, what is the measure of angle C?
(1 point)
Responses
25°
25°
55°
55°
80°
80°
100°
Since triangle A B C is congruent to triangle D E F, angle A is congruent to angle D. So, if angle A is 55 degrees, then angle D is also 55 degrees. Therefore, the measure of angle C is also 55 degrees.
The correct answer is 55°.
To find the measure of angle C in triangle ABC, we can use the fact that congruent triangles have corresponding angles that are equal.
Given that triangle ABC is congruent to triangle DEF, we can say that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F.
From the given information, we know that angle A measures 55 degrees and angle E measures 25 degrees.
Since angle A is congruent to angle D, we can conclude that angle D also measures 55 degrees.
Using the fact that the sum of angles in a triangle is 180 degrees, we can find the measure of angle C.
We have: angle A + angle B + angle C = 180 degrees.
Substituting the values we know, we have: 55 degrees + angle B + angle C = 180 degrees.
To find the measure of angle C, we can subtract the known angles from 180 degrees:
155 degrees + angle C = 180 degrees.
Subtracting 155 degrees from both sides, we have:
angle C = 180 degrees - 155 degrees.
Simplifying, we get:
angle C = 25 degrees.
Therefore, the measure of angle C is 25 degrees.
To find the measure of angle C, we need to use the fact that corresponding angles of congruent triangles are equal.
Given that triangle ABC is congruent to triangle DEF and angle A measures 55 degrees, it means that angle D also measures 55 degrees.
Since angle E measures 25 degrees, we can conclude that angle C is equal to angle F, as they are corresponding angles of the congruent triangles.
Therefore, the measure of angle C is 25 degrees.