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 angles definition

Linear - pair angles are adjacent and supplementary. Angle \(a\) and angle \(e\) are not adjacent, so for 2.a) the answer is FALSE.

Step2: Recall alternate - interior angles definition

Alternate - interior angles are between the two parallel lines and on opposite sides of the transversal. Angle \(f\) and angle \(c\) are alternate - interior angles, so for 2.b) the answer is TRUE.

Step3: Recall linear - pair angles definition

Angle \(d\) and angle \(h\) are not adjacent, so they are not linear - pair angles. For 2.c) the answer is FALSE.

Step4: Recall corresponding angles property

Corresponding angles are equal when lines are parallel. Angle \(a\) and angle \(e\) are corresponding angles, so \(a = e\), not \(a + e=180\). For 2.d) the answer is FALSE.

Step5: Recall vertical - angles property

Vertical angles are equal. Angle \(b\) and angle \(d\) are vertical angles, so \(b = d\). For 2.e) the answer is TRUE.

Step6: Find missing angles

Since \(c = 82^{\circ}\), and \(c\) and \(g\) are vertical angles, \(g = 82^{\circ}\). Also, \(c\) and \(h\) are linear - pair angles, so \(h=180 - 82=98^{\circ}\). Since \(a\) and \(c\) are corresponding angles, \(a = 82^{\circ}\), \(b\) and \(c\) are linear - pair angles so \(b = 98^{\circ}\), \(e=a = 82^{\circ}\), \(f = b=98^{\circ}\).

Answer:

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