a Let's start with recalling that if a quadrilateral is a parallelogram, then its consecutive angles are supplementary. In our exercise, we are given that m∠ NMQ=32 and asked to find m∠ MNP. Let m∠ MNP be represented by x.
As we can see, ∠ NMQ and ∠ MNP are consecutive angles in this parallelogram. Therefore, the sum of the measures of these two angles is equal to 180, as they are supplementary angles.
b Now, we will start with recalling that if a quadrilateral is a parallelogram, then its opposite angles are congruent. In our exercise, we are given that m∠ MQP=125 and asked to find m∠ MNP. Let m∠ MNP be represented by x.
As we can see, ∠ MNP and ∠ MQP are opposite angles in this parallelogram. Therefore, these two angles have the same measure.
x= 125
m∠ MNP =125
c We will begin with recalling that if a quadrilateral is a parallelogram, then its opposite sides are congruent. In our exercise, we are given that the length of MQ is 4, and asked to find the length of NP. Let the length of NP be represented by x.
As we can see, NP and MQ are opposite sides in this parallelogram. Therefore, these two sides have the same length.
x= 4
NP =4
