Question

Given l\\m and m<1= <60 and m1 = 60°, select all angles that are also equal to 60°.

8
2
6
7
5
4

Answer 1

Since line l and line m are parallel lines, all the angles that are also equal to 60° include the following:

B. 2

F. 4

G. 3

In Mathematics and Euclidean Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two lines intersect each other are always congruent, which means being equal to each other.

By applying the vertical angles theorem to the lines, we have the following congruent angles:

m∠1 ≅ m∠2 = 60°

By applying the corresponding angles theorem to the lines, we have the following congruent angles:

m∠1 ≅ m∠3 = 60°

By applying the alternate exterior angles theorem to the lines, we have the following congruent angles:

m∠1 ≅ m∠4 = 60°

Answer 2

Angle 2, angle 3 and angle 4 will measure 60°

Explanation:

From the figure attached,

'l' and 'm' are parallel lines and 't' is the transverse line.

m∠1 = m∠2 = 60° [Vertical angles]

m∠1 = m∠3 = 60° [Corresponding angles]

m∠1 = m∠4 = 60° [Alternate exterior angles]

Therefore, angle 2, angle 3 and angle 4 will measure the same as angle 1.