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?
Answers
Answer:
its 82
Step-by-step explanation:
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.
