Question

Angles with measures 2y + 6 and 8y - 10 are vertical angles. What is their measure?

Answer 1

To find the measure of the vertical angles 2y + 6 and 8y - 10, you set the two expressions equal to each other and solve for 'y', which yields an angle measure of approximately 11.33 degrees for both angles.

Step-by-step explanation:

When two angles are vertical angles, they are opposite each other and have the same measure. Therefore, to find the measure of the angles in this question, you can set the expressions for the two angles equal to each other and solve for 'y'. Then use the value of 'y' to find the measure of each angle.

Here is the equation you'll get from setting the two expressions equal:

• 2y + 6 = 8y - 10

To solve for 'y', you'll first combine like terms:

• 6 + 10 = 8y - 2y

Which simplifies to:

• 16 = 6y

Then, dividing both sides by 6 gives you:

• y = 16/6

Now that you have 'y', you can plug it into either of the original equations to find the measure of the angles:

• 2(16/6) + 6 = 32/6 + 6 = 5.33 + 6 = 11.33 degrees (approximately)

Since the two angles are vertical angles, both angles have the same measure of 11.33 degrees (approximately).