Question

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?

Answer 1

82

Explanation:

Formula: (10x + 8)Angle 1 = (12x - 10)Angle 3

12x - 10x= 8 -(-10)

2x=18

9

you only need to insert the x value (9) into one equation because angles 1 and 3 are CONGRUENT.

(10 x 9) + 8 = ?

90 + 8= 98

and to solve the question, 180 - 98= 82.

82 is the answer

Answer 2

82°

Explanation:

The given angles are vertical angles, so have the same measure:

(10x +8) = (12x -10

18 = 2x . . . . . . . . . . add 10-10x

9 = x

10x +8 = 10(9) +8 = 98

So, angles 1 and 3 measure 98°. Angles 2 and 4 are the supplement of this, so ...

∠2 = 180° -98° = 82°