Question

1. which angle is congruent to Angle 1?

Answer 1

Answer:

1) (b) Angle 5

2) (d) Alternate Exterior Angles Theorem

3) (a) 42 degrees

Step-by-step explanation:

   Given :  A pair of parallel line f and g with z as transversal.

1)  To find angle congruent to angle 1.

• Congruent angles are those angles having same  measurement.

• Corresponding angles are those angles that lies in same position on different parallel lines sharing relative positions.

Out of given options only angle 5 is congruent to angle 1 as they form a pair of corresponding angles and measure of corresponding angles are always equal.

2) To find the theorem that can be used directly to  prove that

Angle 1 ≅ Angle 8

Alternate Exterior Angles Theorem states that for a pair of parallel lines the angles that lies to the exterior and are opposite to each other are congruent to each other.

Since,  angle 1 and angle 8 lies on exterior of parallel lines and are opposite to each other , so Alternate Exterior Angles Theorem is used to prove  Angle 1 ≅ Angle 8.

3) m∠5 = 42° we have to find the m∠4.

Since angle 5 and angle 4 forms a pair of alternate interior angle.

The angle forms when a pair of parallel lines cuts by a trasnversal and the angles that lies lies inside the parallel lines on same side of transversal are alternate interior angles.

Thus, m∠5 = 42° = m∠4

m∠4 = 42°

Answer 2

Part 1) which angle is congruent to Angle 1?

we know that

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles

m∠5=m∠1 ----------> by corresponding angles postulate

therefore

the answer Part 1) is

Angle $5$

Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?

we know that

Alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.

in this problem

m∠1=m∠8 -------> by alternate exterior angles theorem

therefore

the answer part 2) is the option

Alternate Exterior Angles Theorem

Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?

we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal

m∠4=m∠5 --------> by alternate interior angles theorem

so

m∠4=$42\ degrees$

therefore

the answer Part 3) is

$42\ degrees$