There are two vertical angles in a figure with measures m∠1=(2x−16)° and m∠2=98° . What equation will solve for x ?

Question

__x° -__ =__°

Answer 1

In a figure with two vertical angles, the vertical angles are always congruent. Therefore, we can set up the equation:

m∠1 = m∠2

(2x - 16)° = 98°

This equation can be used to solve for x.

Answer 2

Two intersecting lines create four angles; ∠2 and ∠4 are a vertical pair. Their sum of their measures is equal to 110° . What equation will solve for the value of each angle?

__x° =__°

Answer 3

If ∠2 and ∠4 are a vertical pair, then they are congruent. Let's denote their measure as x.

The sum of their measures is given as 110°, so we can set up the equation:

x + x = 110°

This equation can be used to solve for the value of each angle.

Answer 4

Use the image to answer the question.

An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.

m∠1=125° and m∠4=(x+35)° What equation will solve for x ?

x° + __° =__°

Answer 5

In the given figure, ∠1 and ∠4 are vertical angles. Vertical angles are always congruent. Therefore, we can set up the equation:

m∠1 = m∠4

125° = x + 35°

This equation can be used to solve for x.

To write the equation in the requested form, we can rearrange the equation as:

x + 35° = 125°

So, the equation that will solve for x is x + 35° = 125°.

Answer 6

Two angles in a vertical pair have measures that add to 70° . What is the measure of each angle?

__°

Answer 7

In a vertical pair, the angles are congruent, which means they have the same measure.

Let x be the measure of each angle.

According to the given information, the measures of the two angles add up to 70°.

Therefore, we can set up the equation:

x + x = 70°

Simplifying the equation, we have:

2x = 70°

Now, we can solve for x by dividing both sides of the equation by 2:

x = 35°

So, each angle has a measure of 35°.

Answer 8

In a geometric figure two intersecting lines create four angles, where ∠1 and ∠3 are a vertical pair. If m∠1=(3x−25)° and m∠3=104° , what is the value of x ?

__

Answer 9

Since ∠1 and ∠3 are a vertical pair, they are congruent. We can set up the equation:

m∠1 = m∠3

(3x - 25)° = 104°

To solve for x, we can isolate x by adding 25 to both sides of the equation:

3x - 25 + 25 = 104 + 25

3x = 129

Then, we divide both sides of the equation by 3 to solve for x:

x = 129 / 3

Simplifying the expression:

x = 43

Therefore, the value of x is 43.

Answer 10

There is a pair of vertical angles whose measures are m∠1=106° and m∠2=(3x−75)° . What equation can you write to solve for x ?

3x° - 75° + 106° = 180°
3x° - 75° = 106°
3x° -75° - 106° = 180°
3x° - 75° + 106° = 90°

Answer 11

To solve for x, we need to recognize that vertical angles are congruent. Therefore, we can set up the equation:

m∠1 = m∠2

106° = 3x - 75°

This equation can be used to solve for x.