Question

PLEASE HELP ME OUT 75 POINTS!

Determine the value of x, and the measure of angle A:



x =

m

Answer 1

• x = 7
• A = 157°

Explanation:

Vertically opposite angles are two angles that are opposite each other when two lines intersect. They are also called vertical angles.

Vertically opposite angles are always equal in measure.

In this case:

(x + 16)° and (4x - 5)° are vertically opposite angles.

So,

(x + 16)° = (4x - 5)°

x + 16 = 4x - 5

Subtract x on both sides.

x + 16 - x = 4x - 5 - x

16 = 3x - 5

Add 5 on both sides:

16 + 5 = 3x - 5 + 5

21 = 3x

Divide both sides by 3.

`\sf (21)/(3)=(3x)/(3)`

7 = x.

Therefore,

Value of x is 7.

And

(x + 16)° and A are angles of linear pair. And Linear pair angles are supplementary means added up to 180°.

So,

(x + 16)° + A = 180°

Substitute the value of x.

(7 + 16)° + A = 180°

23° + A = 180°

Subtract 23° on both sides.

23° + A - 23° = 180° - 23°

A = 157°

Therefore, the measure of angle A is 157°.

Answer 2

x = 7 , ∠ A = 157°

Explanation:

(4x - 5)° and (x + 16)° are vertically opposite angles and are congruent ( equal ), then

4x - 5 = x + 16 ( subtract x from both sides )

3x - 5 = 16 ( add 5 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

-------

Then

4x - 5 = 4(7) - 5 = 28 - 5 = 23°

∠ A and 4x - 5 are a linear pair and sum to 180° , that is

∠ A + 23° = 180° ( subtract 23° from both sides )

∠ A = 157°