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Parallelograms
A
B
C
D
E
. . . .

Properties of Parallelograms (2)

You can now solve the next problems using the properties of a parallelogram.

Example 1

In parallelogram MIND, the measure of ∠M is 75 ∘ . What are the measures of the other angles?


Solution

Consecutive angles of a parallelogram are supplementary and so, m∠M+m∠D= 180 ∘ .

75 ∘ +m∠D = 180 ∘
m∠D = 180 ∘ − 75 ∘
= 105 ∘

Opposite angles of a parallelogram are congruent and so, m∠M=m∠N= 75 ∘ . Also, m∠D=m∠I= 105 ∘ .