Question

Find the values of the missing sides in the parallelogram given.

Answer 1

Given:

m∠B = 44°

Let's find the following measures:

m∠A, m∠BCD, m∠CDE

We have:

• m∠A:

Angle A and Angle B are interior angles on same side of a transversal.

The interior angles are supplementary.

Supplementary angles sum up to 180 degrees

Therefore, we have:

m∠A + m∠B = 180

m∠A + 44 = 180

Subtract 44 from both sides:

m∠A + 44 - 44 = 180 - 44

m∠A = 136°

• m,∠,BCD:

m∠BCD = m∠A

Thus, we have:

m∠BCD = 136°

• m∠CDE:

Angle C and angle CDE form a linear pair.

Linear pair of angles are supplementary and supplementary angle sum up to 180 degrees.

Thus, we have:

m∠D = m∠B

m∠D = 44°

m∠CDE + m∠D = 180

m∠CDE + 44 = 180

Subract 44 from both sides:

m∠CDE + 44 - 44 = 180 - 44

m∠CDE = 136°

ANSWER:

• m∠A = 136°

,

•

,

• m∠BCD = 136°

,

•

,

• m∠CDE = 136°