Question

Can somebody please answer these 3 questions please and thank you

Answer 1

`\displaystyle \boxed{\text{First Attachment, 14}}`

Answer:

x = 30

y = 60

Explanation:

First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.

Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.

Lastly, corresponding angles on parallel lines are congruent.

By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.

`\displaystyle \boxed{\text{Second Attachment, 12}}`

Answer:

x = 65

Explanation:

From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.

We also know there are 180 degrees in a triangle.

Lastly, we know that alternate interior angles are congruent.

Using this knowledge, we can decide that x = 65.

`\displaystyle \boxed{\text{Third Attachment, 13}}`

Answer:

x = 30

Explanation:

Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.

After placing vertical angles down from the given information, we can fill in more using corresponding angles.

Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.

Using this information, we can decide that x = 30.