Angle Properties - Parallel Lines Quiz

 Angle “b” and 40 degrees are alternate angles. Alternate angles are equal to each other. Thus, angle b is also 40 degrees. 

The given answer "63, sixty three, sixtythree" indicates that angle a measures 63 degrees. The angles are vertical, which means they are equal to each other. Thus, if one angle is 63 degrees, then so is the other angle.

The size of angle g is 70°. Both angles are alternate, which means they are equal to each other. Thus, angle “g” is also 70 degrees.

Angle “c” and 120 degrees are alternate angles, which means they are equal. Thus, angle “c” is also 120.

The size of angle d is 55°. Angle b and 55 degrees are vertical angles, which means they are equal. Thus, angle b is 55. However, angle b and angle d are corresponding angles. Corresponding angles are equal to each other. Thus, angle d is 55. 

Angle “a” and 120 degrees are vertical angles, which means they are equal. Thus, angle “a” is also 120.

The correct answer is 55 because angle g and 55 degrees are corresponding angles, which means they are equal. 

To find the measure of angle f, observe the relationships between the angles in the diagram.

You're given that angle h = 40°.

Since the two lines are parallel and crossed by a transversal, we can use angle relationships such as:

Alternate interior angles

Corresponding angles

Vertical angles

Linear pairs (supplementary)

Step-by-step:

Angle h and angle f are corresponding angles, because they lie on the same side of the transversal and in the same relative position at each intersection.

Corresponding angles are equal when the lines are parallel.

Therefore:

Angle f = 40°

✅ Final Answer: 40°

70 degrees and angle “c” are co-interior angles. They add up to equal 180. Thus, to determine what angle “c” is we will subtract 70 from 180, which gives us 110.

Angles a and c are corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines. In this case, the angles a and c are located in the same position on the two parallel lines, one on each line. Corresponding angles have equal measures, so angle a and angle c are equal.

Identify the relationships between the angles:

The angles marked 120° and 'e' are supplementary angles (they add up to 180°).

Angles 'e' and 'd' are alternate interior angles. Alternate interior angles are formed when a transversal line intersects two parallel lines. They are located on opposite sides of the transversal and inside the parallel lines.  

2. Find the measure of angle 'e':

Since the 120° angle and angle 'e' are supplementary:

e + 120° = 180° e = 60°  

3. Find the measure of angle 'd':

When a transversal intersects two parallel lines, alternate interior angles are congruent (equal). Therefore:

d = e d = 60°

Therefore, angle d measures 60°.

Angles b and c are co-interior angles because they are located on the same side of the transversal line and on the inside of the two parallel lines. Co-interior angles are supplementary, which means that their sum is equal to 180 degrees. In this case, angles b and c add up to 180 degrees, indicating that they are co-interior angles.

Vertically-opposite angles are formed when two lines intersect. In this case, angles a and b are formed by the intersection of two lines. Vertically-opposite angles are always equal to each other, meaning that angle a is equal to angle b. This is why the answer is vertically-opposite.

Angle f and 40 degrees are co-interior angles. Co-interior angles are supplementary, which means they add up to equal 180. Thus, we will subtract 40 from 180 to determine that angle f is 140 degrees. However, angle “a” and angle “f” are vertical angles, which means they are equal. Thus, if angle f is 140, then angle “a” is also 140.

Angles b and g are alternate angles. Alternate angles are formed when a transversal intersects two parallel lines. In this case, the angles b and g are on opposite sides of the transversal and on different parallel lines. Alternate angles are congruent, meaning they have the same measure.