Question

1.) List all interior angles (see image)

2.) Identify all pairs of corresponding angles.

3.) What is the relationship between angles D and E?

4.) If Angle B= 75 degrees, identify the following angle measurements
Angle A=
Angle C=
Angle D=
Angle E=
Angle F=
Angle G=
Angle H=

5.) List all angles congruent to angle G.

6.) If angle F is 115 degrees, what is the measure of angle B?

Answer 1

1. Interior angles:- B and F

C and G

2. Corresponding angles:- E and G

F and H

A and C

B and D

3. Equal

4. Angle A = 105

Angle C = 105

Angle D = 75

Angle E = 75

Angle F = 105

Angle G = 75

Angle H = 105

5. Angle D

6. Angle B = 65

Explanation:

1. The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles.

∴ Pair of interior angles are:- 1) B and F

2) C and G

2. Corresponding angles:- the angles which occupy the same relative position at each intersection where a straight line crosses two others.

∴ Pair of corresponding angles:- 1) A and C

2) B and D

3) E and G

4) F and H

3. Angle D and E are equal as they form alternate exterior angles.

4. Angle B = 75 degrees

Angle A = (180-B) = 105 degrees

Angle C = (180-B) = 105 degrees(interior angles)

Angle D = B = 75 degrees(corresponding angles)

Angle E = B = 75 degrees(congruent angles)

Angle F = (180-B) = 105 degrees

Angle G = B = 75 degrees(alternate interior angles)

Angle A = (180-B) = 105 degrees

5. Angle D

6. Angle F = 115 degrees

Angle B = (180-115) = 65 degrees