Exercise 1 Page 407

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 ∠ N M Q = 32

and asked to find

m ∠ M N P .

Let

m ∠ M N P

be represented by

x .

As we can see,

∠ N M Q

and

∠ M N P

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.

32 + x = 180

SubEqn

$LHS - 32 = RHS - 32$

x = 148

The measure of

∠ M N P

148 .

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 ∠ M Q P = 125

and asked to find

m ∠ M N P .

Let

m ∠ M N P

be represented by

x .

As we can see,

∠ M N P

and

∠ M Q P

are opposite angles in this parallelogram. Therefore, these two angles have the same measure.

x = 125 m ∠ M N P = 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

M Q

4,

and asked to find the length of

N P .

Let the length of

N P

be represented by

x .

As we can see,

N P

and

M Q

are opposite sides in this parallelogram. Therefore, these two sides have the same length.

x = 4 \overline{N P} = 4

Subchapter links

Check Your Understanding p.407

H.O.T. Problems p.410

Standardized Test Practice p.411

Spiral Review p.411

Skills Review p.411