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∠A and \angle B∠B are vertical angles. If m\angle A=(x+16)^{\circ}∠A=(x+16)​​ and m\angle B=(3x-14)^{\circ}∠B=(3x−14), then find the measure of \angle A∠A.

Respuesta :

sqdancefan

The measures of vertical angles are identical.


∠A = ∠B

x+16 = 3x-14 . . . . substitute the given measures

30 = 2x . . . . . . . . add 14-x

15 = x . . . . . . . . . .divide by 2


∠A = ∠B = 15+16 = 31


The measure of ∠A is 31°.

akposevictor

The measure of angle A is 31 degrees.

Given:

[tex]m\angle A=(x+16)^{\circ}\\m\angle B=(3x-14)^{\circ}[/tex]

Note:

Vertical angles are always congruent to each other.

Since angle A and angle B are vertical angles, therefore:

[tex]m\angle A = m\angle B[/tex]

Substitute:

[tex]x+16 = 3x-14[/tex]

Solve for x

[tex]14+16 = 3x-x\\30 = 2x[/tex]

Divide both sides by 2

[tex]15 = x\\x = 15[/tex]

Find [tex]m\angle A[/tex]

[tex]m\angle A=(x+16)^{\circ}\\[/tex]

Plug in the value of x

[tex]m\angle A= (15+16)^{\circ}\\\\m\angle A= 31^{\circ}[/tex]

Therefore the measure of angle A is 31 degrees.

Learn more about vertical angles here:

https://brainly.com/question/18292462