Question

11. Determine the measure of the angles below.

12. Two lines intersect to form the four angles shown in the figure. Which term does not accurately describe the pair of angles 1 and 4?

Answer 1

Problem 11

Answers:

• 5x+20 = 125
• 3x-8 = 55

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Step-by-step explanation:

The two angles shown here form a linear pair. They supplementary so they add to 180.

(5x+20)+(3x-8) = 180

(5x+3x) + (20-8) = 180

8x+12 = 180

8x = 180-12

8x = 168

x = 168/8

x = 21

We then find the angles to be

5x+20 = 5*21+20 = 125

3x-8 = 3*21-8 = 55

Note how 125+55 = 180 to help confirm the answers

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Problem 12

Answer: B) Vertical angles

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Step-by-step explanation:

Vertical angles are angles that form after intersecting two lines, and the angles are opposite one another. So one example of a vertical angle pairing would be angles 1 and 3. The other vertical angle pair of this diagram are angles 2 and 4. Vertical angles are always congruent to one another.

In this diagram, angles 1 and 4 are adjacent since they are next to each other. In other words, they share a common line (think of apartment neighbors sharing a common wall). Since they are adjacent angles, there is no way they are vertical angles.

Angles 1 and 4 are also supplementary since they form a straight line. They are a linear pair for very similar reasons. This allows us to rule out choices A, C and D.

Side note: the term "linear pair" means that the angles are adjacent and supplementary.

Answer 2

11 - 125 and 55

12 - supplementary

Step-by-step explanation:

5x+20+3x-8=180

step 1 combine like terms

8x+12=180

step 2 subtract 12 from each side

8x=168

step 3 divide each side by 8

x=21

then you just plug in 21 to each equation to find that angle 1 = 125 and angle 2=55