Solving Equations with Vertical Angles

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1) If ∠x = 3y + 5 and ∠y = 50, and the two angles are vertical, what is the value of y?

Explanation

Vertical angles are equal. Set 3y + 5 = 50.

So, 3y = 45 → y = 15.

The value of y is 15.

Submit
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About This Quiz
Solving Equations With Vertical Angles - Quiz

Can you combine algebra and geometry? In this quiz, you’ll solve equations based on the fact that vertical angles are always equal. You’ll begin with straightforward setups and then tackle multi-step problems involving angles that form straight lines. Using what you know about vertical and supplementary angles, you’ll find missing... see morevalues while seeing how algebra and geometry work hand in hand. see less

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2) Two vertical angles are given as (2x + 10)° and (4x – 30)°. Find the measure of each angle.

Explanation

Vertical angles are equal. Set 2x + 10 = 4x − 30.

So, 40 = 2x → x = 20. Each angle = 2(20) + 10 = 50°.

Each angle measures 50°.

Submit
3) If ∠A = 5x + 15 and ∠B = 95, and ∠A and ∠B are vertical angles, what is x?

Explanation

Vertical angles are equal. Set 5x + 15 = 95.

So, 5x = 80 → x = 16.

The value of x is 16.

Submit
4) ∠1 = (6y – 20)°, ∠2 = (4y + 10)°. If ∠1 and ∠2 are vertical, then what is y?

Explanation

Vertical angles are equal. Set 6y − 20 = 4y + 10.

So, 2y = 30 → y = 15.

The value of y is 15.

Submit
5) Two vertical angles are represented as (x + 30)° and (2x – 60)°. What is the value of x?

Explanation

Vertical angles are equal. Set x + 30 = 2x − 60.

So, x = 90.

The value of x is 90.

Submit
6) If one vertical angle is (7x – 25)° and the other is (5x + 15)°, find the value of x.

Explanation

Vertical angles are equal. Set 7x − 25 = 5x + 15.

So, 2x = 40 → x = 20.

The value of x is 20.

Submit
7) ∠M = (3a + 5)°, ∠N = (2a + 25)°. If ∠M and ∠N are vertical, then what is a?

Explanation

Vertical angles are equal. Set 3a + 5 = 2a + 25.

So, a = 20.

The value of a is 20.

Submit
8) If vertical angles are expressed as (x – 10)° and (2x – 40)°, what is x?

Explanation

Vertical angles are equal. Set x − 10 = 2x − 40.

So, x = 30.

The value of x is 30.

Submit
9) Two vertical angles are (4b – 5)° and (3b + 10)°. Find the measure of each angle.

Explanation

Vertical angles are equal. Set 4b − 5 = 3b + 10.

So, b = 15. Each angle = 4(15) − 5 = 55°.

Each angle measures 55°.

Submit
10) ∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair. If ∠1 = 3x + 6 and ∠3 = x + 66, find the measures of ∠1, ∠2, ∠3 (in that order).

Explanation

Vertical: ∠1 = ∠2. Linear pair: ∠2 + ∠3 = 180.

Set 3x + 6 + (x + 66) = 180 → 4x + 72 = 180 → x = 27.

∠1 = 3(27) + 6 = 87°, ∠2 = 87°, ∠3 = 27 + 66 = 93°.

The measures are 87°, 87°, 93°.

Submit
11) Vertical angles are written as (12 + 2x)° and (3x – 6)°. What is the measure of the angles?

Explanation

Vertical angles are equal. Set 12 + 2x = 3x − 6.

So, x = 18. Angle = 12 + 2(18) = 48°.

Each angle measures 48°.

Submit
12) ∠P = (6k – 12)°, ∠Q = (4k + 8)°. If P and Q are vertical, find k.

Explanation

Vertical angles are equal. Set 6k − 12 = 4k + 8.

So, 2k = 20 → k = 10.

The value of k is 10.

Submit
13) If ∠x = (5m + 7)° and ∠y = (6m – 3)°, find the angle measure if x and y are vertical.

Explanation

Vertical angles are equal. Set 5m + 7 = 6m − 3.

So, m = 10. Angle = 5(10) + 7 = 57°.

Each angle measures 57°.

Submit
14) Two vertical angles are expressed as (2x + 25)° and (75 + x)°. Find x.

Explanation

Vertical angles are equal. Set 2x + 25 = 75 + x.

So, x = 50.

The value of x is 50.

Submit
15) If ∠A = (x + 12)° and ∠B = (2x – 18)°, and ∠A = ∠B, find the measure of each.

Explanation

Set x + 12 = 2x − 18.

So, x = 30. Each angle = 30 + 12 = 42°.

Each angle measures 42°.

Submit
16) ∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair. If ∠1 = 4y + 8 and ∠3 = 2y + 52, find the measures of ∠1, ∠2, ∠3 (in that order).

Explanation

Vertical: ∠1 = ∠2. Linear pair: ∠2 + ∠3 = 180.

Set (4y + 8) + (2y + 52) = 180 → 6y + 60 = 180 → y = 20.

∠1 = 4(20) + 8 = 88°, ∠2 = 88°, ∠3 = 2(20) + 52 = 92°.

The measures are 88°, 88°, 92°.

Submit
17) Two vertical angles are (x – 3)° and (2x – 23)°. Find the measure of each.

Explanation

Vertical angles are equal. Set x − 3 = 2x − 23.

So, x = 20. Each angle = 20 − 3 = 17°.

Each angle measures 17°.

Submit
18) ∠1 and ∠2 are vertical angles. ∠1 = (11n – 15)°, ∠2 = (7n + 21)°. Solve for n.

Explanation

Vertical angles are equal. Set 11n − 15 = 7n + 21.

So, 4n = 36 → n = 9.

The value of n is 9.

Submit
19) If vertical angles ∠R = (4x + 12)° and ∠S = (6x – 18)°, find the value of x.

Explanation

Vertical angles are equal. Set 4x + 12 = 6x − 18.

So, 30 = 2x → x = 15.

The value of x is 15.

Submit
20) Two vertical angles are written as (5p – 2)° and (3p + 18)°. What is p?
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If ∠x = 3y + 5 and ∠y = 50, and the two angles are vertical,...
Two vertical angles are given as (2x + 10)° and (4x –...
If ∠A = 5x + 15 and ∠B = 95, and ∠A and ∠B are...
∠1 = (6y – 20)°, ∠2 = (4y + 10)°. If ∠1 and...
Two vertical angles are represented as (x + 30)° and (2x –...
If one vertical angle is (7x – 25)° and the other is (5x +...
∠M = (3a + 5)°, ∠N = (2a + 25)°. If ∠M and ∠N...
If vertical angles are expressed as (x – 10)° and (2x...
Two vertical angles are (4b – 5)° and (3b + 10)°. Find...
∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair....
Vertical angles are written as (12 + 2x)° and (3x – 6)°....
∠P = (6k – 12)°, ∠Q = (4k + 8)°. If P and Q are...
If ∠x = (5m + 7)° and ∠y = (6m – 3)°, find the...
Two vertical angles are expressed as (2x + 25)° and (75 + x)°....
If ∠A = (x + 12)° and ∠B = (2x – 18)°, and...
∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair....
Two vertical angles are (x – 3)° and (2x – 23)°....
∠1 and ∠2 are vertical angles. ∠1 = (11n – 15)°,...
If vertical angles ∠R = (4x + 12)° and ∠S = (6x –...
Two vertical angles are written as (5p – 2)° and (3p +...
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