Angle Terminology with Equations

Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, x, plus, 17, right bracket, degrees∠1=(x+17)∘ and mangle, 2, equals, left bracket, 2, x, minus, 26, right bracket, degrees∠2=(2x−26)∘, then find the measure of angle, 1∠1.

Answer 1

Hi Alli,

Thanks for the question. If you would like to review this or anything else, I'm happy to provide your first session free.

The final answer to this question is The measure of angle ∠1 is 60 degrees.

Please see explanation and step-by-step work below.

Let's first dive into some angle terminology with equations to find the measure of angle ∠1.

First, we're given that ∠1 and ∠2 are vertical angles. Vertical angles are opposite angles formed when two lines intersect. They are always congruent, meaning they have the same measure. In this case, ∠1 and ∠2 have the same measure.

Now, we have expressions for the measures of these angles:

∠1 = (x + 17) degrees ∠2 = (2x - 26) degrees

Since ∠1 and ∠2 are congruent, we can set these two expressions equal to each other:

(x + 17) = (2x - 26)

Now, we need to solve for x. Let's simplify the equation step by step:

First, let's get rid of the parentheses. Distribute 2 on the right side:

x + 17 = 2x - 26

Next, let's isolate x on one side of the equation. You can do this by moving all terms involving x to one side and constants to the other side. Let's subtract x from both sides:

17 = x - 26

Now, add 26 to both sides to solve for x:

17 + 26 = x

43 = x

So, we've found that x is equal to 43 degrees.

Now that we know the value of x, we can find the measure of ∠1:

∠1 = (x + 17) degrees ∠1 = (43 + 17) degrees ∠1 = 60 degrees

The measure of angle ∠1 is 60 degrees.

Hope this helps & hope to hear from you soon.

Thank you,

Benjamin M.

Answer 2

What is true about the measures of two vertical angles?