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

Answer:

its 82

Step-by-step explanation:

Answer 2

Given,

2 lines intersect forming 4 angles.

∠1 = (10x + 8) degrees,

∠3 = (12x - 10) degrees.

To find,

m ∠2.

Solution,

Firstly, it is given here that 4 angles are formed by 2 intersecting lines. Angles are 1, 2, 3, and 4 respectively, clockwise from the top left.

The angles formed are shown in the figure.

Here, it is given that,

∠1 = 10x + 8, and,

∠3 = 12x - 10

Now, it can be seen that ∠1 and ∠3 being vertically opposite angles, must be equal. Thus,

∠1 = ∠3

⇒ 10x + 8 = 12x - 10

Rearranging and simplifying, we get,

2x = 18

⇒ x = 9.

Since ∠1 = 10x + 8,

∠1 can be determined by putting the above value of x here. So,

as ∠1 = 10x + 8

⇒ ∠1 = 10(9) + 8

⇒ ∠1 = 98°.

It can be seen from the figure that, ∠1 and ∠2 form a linear pair. Thus,

∠1 + ∠2 = 180°

⇒ ∠2 = 180 - 98

⇒ ∠2 = 82°.

Therefore, the measure of angle 2 in degrees will be 82.