Question

What are the numerical measures of each angle in the diagram?

∠1 and ∠3 measure
degrees.

∠2 and ∠4 measure
degrees.

Answer 1

29 degrees and 151 degrees!

Explanation:

Answer 2

∠1 = 29 degrees

∠2 = 151 degrees

∠3 = 29 degrees

∠4 = 151 degrees

Explanation:

By look at the figure, ∠1 and ∠3 are opposite angles.

Opposite angles are equal.

Given: ∠1 = 3x -1 and ∠2 = 2x + 9

Therefore, by the property

3x - 1 = 2x + 9

We can find x.

3x - 2x = 9 +1

1x = 10

x = 10

By plugging in x =10 in the above expression, we get

∠1 = 3(10) - 1

∠1 = 30 -1

∠1 = 29 degrees.

∠3 = 29 degrees.

∠2 and∠4 are equal since they are opposite angles.

Let's find ∠2

∠2 + ∠1 = 180 degrees since there are in a straight line.

∠2 + 29 = 180

∠2 = 180 -29

∠2 = 151 degrees.

∠4 = 151 degrees

Hope this will helpful.

Thank you.