Answer:
We conclude that:
m∠B = 101°
m∠C = 79°
m∠D = 101°
Step-by-step explanation:
Given the parallelogram ABCD
We know that a parallelogram has opposite angles that are congruent.
Here,
The angles ∠A and ∠C are opposite angles.
Thus,
The angles ∠B and ∠D are opposite angles.
Thus,
Determining the measure of angles of a parallelogram:
As
∠A = 79°
We know
Thus, the measure of the angle ∠C is:
m∠C = 79°
We know that the sum of the measure of two consecutive angles is 180°.
As ∠A and ∠D are consecutive angles, so
∠A + ∠D = 180°
substituting ∠A = 79° in the equation
79° + ∠D = 180°
subtracting 79° from both sides
79° + ∠D - 79° = 180° - 79°
∠D = 101°
Thus, the measure of the angle D is:
m∠D = 101°
We know that the angles ∠B and ∠D are opposite angles.
Thus,
so if m∠D = 101° then ∠B is also 101°.
Therefore, the measure of angle B is:
m∠B = 101°
Hence, we conclude that:
m∠B = 101°
m∠C = 79°
m∠D = 101°
