Question

Parallel lines A and B are cut by transversal t. If m∠1= 85, what is the measure of ∠5?

Show your solution.​

Answer 1

Answer:

a and b are parallel lines and line l is transversal to a and b. So, angle 1 = angle 7. As vertically opposite angles are equal, angle 7 = angle 5.

So, angle 1 = angle 5. So, angle 5 = angle 1.

Angle 5 = 85°

Answer 2

Given:

m∠1= 85°

To find:

The measure of angle 5

Solution:

The value of angle 5 is 85°.

Since lines b and a are parallel, certain angles will be equal.

Angle 1=Angle 3 (Vertically opposite to each other)

∠1=∠3= 85°

Angle 3 and Angle 8 are supplementary.

So, angle 3+angle 8=180°

∠3+∠8=180°

85°+∠8=180°

∠8=180°-85°

∠8=95°

Similarly, angle 8 and angle 5 form a linear pair.

Angle 8+angle 5=180°

95°+∠5=180°

∠5=180°-95°

∠5=85°

Therefore, the value of angle 5 is 85°.