∠A and ∠B are vertical angles with m∠A = x and m∠B = 5x - 80 What is m∠A ?

Solution:

Given, ∠A and ∠B are vertical angles.

Let the measure of ∠A = x

∠B = 5x - 80.

We have to find the measure of ∠A.

Vertical angles are a pair of opposite angles formed by intersecting lines.

In the figure, x and  5x-80 are vertical angles. Since vertically opposite angles are always equal, m∠A = m∠B.

Vertical angles are always congruent. So, in this figure, ∠A ≅ ∠B

So, ∠A = ∠B

x = 5x - 80

By grouping,

x - 5x = -80

-4x = - 80

4x = 80

x = 80/4

x = 20

So, ∠A = x = 20 degrees

Therefore, the value of ∠A is 20 degrees.

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∠A and ∠B are vertical angles with m∠A = x and m∠B = 5x - 80 What is m∠A ?

Summary:

∠A and ∠B are vertical angles with m∠A = x and m∠B = 5x - 80, then m∠A = 20 degrees.