Question

You now know a lot about all the angles formed from two straight lines that intersect. You know which angles are congruent and which angles are supplementary. Based on this information, you can find the angle measurements of all the angles even when you only know the measurement of one angle. In the figure below, angle 2 measures 145 degrees. What are the measurements of angles 1, 3 and 4? A angle 1 = 35 degrees, angle 3 = 145 degrees, angle 4 = 35 degrees B angle 1 = 30 degrees, angle 3 = 30 degrees, angle 4 = 160 degrees C angle 1 = 35 degrees, angle 3 = 35 degrees, angle 4 = 145 degrees D angle 1 = 135 degrees, angle 3 = 145 degrees, angle 4 = 35 degrees

Answer 1

Using the properties of angles formed from two straight lines that intersect, we can find the measurements of angles 1, 3, and 4 by determining their relationships to angle 2.

Step-by-step explanation:

To find the measurements of angles 1, 3, and 4, we can use the properties of angles formed from two straight lines that intersect. Angle 1 and angle 3 are alternate interior angles, which means they are congruent. Angle 2 and angle 4 are vertical angles, which means they are congruent as well. Since angle 2 measures 145 degrees, angle 4 also measures 145 degrees. Therefore, the measurements of angles 1, 3, and 4 are: angle 1 = 145 degrees, angle 3 = 145 degrees, angle 4 = 145 degrees. So, the correct option is D. angle 1 = 135 degrees, angle 3 = 145 degrees, angle 4 = 35 degrees.

Answer 2

This is the correct way to set up the equation:

9x + 88 + 6x + 182 = 180

I'm going to move some things around so we can combine like terms. It now reads:

9x + 6x + 88 + 182 = 180

9x + 6x = 15x, so the equation now reads:

15x + 88 + 182 = 180

88 + 182 = 270, so the equation reads:

15x + 270 = 180

Subtract the 270 from both sides. 180 - 270 is -90:

15x = -90

Divide both sides by 15. -90 divided by 15 = -6:

x = -6

Now we can substitute -6 back into the separate equations.

9(-6) + 88 = ?

9 times -6 is -54. -54 + 88 = 34.

6(-6) + 182 = ?

6 times -6 = -36. -36 + 182 = 146

Now we can add 34 and 146 together.

34 + 146 = 180

I hope I helped answer your question!

Step-by-step explanation: