Question

Use the properties of vertical angles to find the value of x.A)3B)5C)7D)92)What is the measure of ∠A?A)157°B)159°C)161°D)163°

Answer 1

PART 1

Option C is correct.

x = 7°

PART 2

Option A is correct.

Angle A = 157°

Step-by-step explanation

Vertical angles are angles that are directly opposite each other at a point where two straight lines intersect. Vertical angles are equal to each other.

Since vertical angles are equal, we can equate (x + 16)° and (4x - 5)° in order to solve for x

(x + 16)° = (4x - 5)°

x° + 16° = 4x° - 5°

x° - 4x° = -5° - 16°

-3x° = -21°

Divide both sides by -3

(-3x°/-3) = )-21°/-3)

x° = 7°

For the second part, we need to note that the sum of angles on a straight line is 180°.

So,

(x + 16°) + Angle A = 180°

x° + 16° + Angle A = 180°

x° = 7°

x° + 16° + Angle A = 180°

7° + 16° + Angle A = 180°

23° + Angle A = 180°

Angle A = 180° - 23°

Angle A = 157°

Hope this Helps!!!