The measure of angle 1 is (10 x + 8) degrees and the measure of angle 3 is (12 x minus 10) degrees.

2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.

What is the measure of angle 2 in degrees?

°

Step-by-step explanation:

I'm assuming by this description that angles 1 and 3 are diagonal from each other. If that be the case, they are vertical angles and that means that they are congruent. In other words, angle 1 = angle 3 AND 10x + 8 = 12x - 10. We can solve for x to find the degree measure of these angles:

10x + 8 = 12x - 10 and

18 = 2x so

x = 9. That means that angles 1 and 3 measure

10 (9) + 8 = 98

98 degrees is the measure of angle 1 and angle 3. That means that angles 1 and 2 are supplementary since they are next to each other (or adjacent, in proper terms). They add to up 180:

angle 1 + angle 2 = 180 and

98 + angle 2 = 180 so

angle 2 = 82

Not only does angle 2 = 82, but since angle 4 is vertical to it, it also measures 82. All 4 angles must add up to equal 360. Let's check that:

98 + 98 + 82 + 82 better equal 360. And it does.