Question

2.) reference the diagram at right to determine whether the following statements are true or false.
a.) angle a and angle e are linear - pair angles. true false
b.) angle f and angle c are alternate interior angles. true false
c.) angle d and angle h are linear - pair angles. true false
d.) a + e = 180 true false
e.) b = d true false
3.) use the diagram below to find the missing angles. show work.
m∠a=
m∠b=
m∠c=
m∠e=
m∠f=
m∠g=
m∠h=

Explanation:

Step1: Recall linear - pair definition

Linear - pair angles are adjacent and supplementary. Angle a and angle e are not adjacent, so they are not a linear - pair. For part a, angle a and angle f are linear - pair angles (adjacent and sum to 180°), so the statement about a and e is FALSE.

Step2: Recall alternate - interior angles

Alternate - interior angles are between two parallel lines and on opposite sides of a transversal. Angle f and angle c are alternate - interior angles, so part b is TRUE.

Step3: Recall linear - pair definition

Angle d and angle h are not adjacent, so they are not linear - pair angles. Part c is FALSE.

Step4: Recall corresponding angles

Corresponding angles are equal when lines are parallel. Angle a and angle e are corresponding angles, so \(a = e\), and \(a + e
eq180\) (unless \(a = e=90^{\circ}\), but no indication of that here), so part d is FALSE.

Step5: Recall vertical - angles

Vertical angles are equal. Angle b and angle d are vertical angles, so \(b = d\), part e is TRUE.

Step6: Find missing angles

Given \(m\angle c = 82^{\circ}\).

• \(m\angle a=m\angle c = 82^{\circ}\) (corresponding angles).
• \(m\angle b = 180 - 82=98^{\circ}\) (linear - pair with \(\angle c\)).
• \(m\angle e=m\angle a = 82^{\circ}\) (corresponding angles).
• \(m\angle f=m\angle b = 98^{\circ}\) (corresponding angles).
• \(m\angle g=m\angle c = 82^{\circ}\) (vertical angles).
• \(m\angle h=m\angle b = 98^{\circ}\) (vertical angles).

Answer:

a. FALSE
b. TRUE
c. FALSE
d. FALSE
e. TRUE
\(m\angle a = 82^{\circ}\)
\(m\angle b = 98^{\circ}\)
\(m\angle c = 82^{\circ}\)
\(m\angle e = 82^{\circ}\)
\(m\angle f = 98^{\circ}\)
\(m\angle g = 82^{\circ}\)
\(m\angle h = 98^{\circ}\)