Question

Can someone please help me with these two math problems about angles?

Answer 1

The math angle for #1 is 2x and #2 is 3 x

Answer 2

First question: x = 19

Second question: p = 75

Explanation:

First, let's solve for x. We already know that one angle measures 105°. According to the Vertical Angles Theorem, two angles that are vertical from each other are congruent. So, the angle vertical from the one we know measures 105° is equal to it. Therefore, we can set up this equation:

5x - 10 = 105

First, add 10 to both sides.

5x = 115

Now, divide both sides by 5 to get x.

x = 23

For the next problem, let's look at 5x - 10 and p. These angles form a linear pair, so their sum is going to be 180°. The instructions say we have to use x, so let's set up this equation to represent it:

5x - 10 + p = 180

Let's go ahead and plug our x-value in.

5(23) - 10 + p = 180

Simplify.

105 + p = 180

Now subtract 105 from both sides to get p.

p = 75