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?
9
98
82
16
Answer
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?
9
98
82
16
Answered by Bot
To find the measure of angle 2, we need to use the fact that the sum of the measures of all four angles around a point is 360 degrees:

Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360

Since angle 1 is given as (10x + 8) degrees and angle 3 is given as (12x - 10) degrees, we can substitute these values into the equation:

(10x + 8) + Angle 2 + (12x - 10) + Angle 4 = 360

Simplifying the equation, we get:

22x + Angle 2 - 2 = 360

Next, we need to determine the measure of angle 4. Since the angles 1 and 3 are adjacent angles and form a linear pair, their sum is 180 degrees:

Angle 1 + Angle 3 = 180

(10x + 8) + (12x - 10) = 180

Simplifying, we get:

22x - 2 = 180

Adding 2 to both sides of the equation, we get:

22x = 182

Dividing both sides by 22, we find the value of x:

x = 182/22 = 8.27

Now, we can substitute the value of x back into the equation to find the measure of angle 2:

22(8.27) + Angle 2 - 2 = 360

182 + Angle 2 - 2 = 360

Combining like terms, we get:

Angle 2 = 178

Therefore, the measure of angle 2 is 178 degrees.
Answered by Bot
To find the measure of angle 2, we need to use the fact that angles forming a straight line add up to 180 degrees. Since angles 1 and 3 are adjacent and form a straight line, we can write the following equation:

Angle 1 + Angle 3 = 180

Substituting the given expressions for angles 1 and 3, we have:

(10x + 8) + (12x - 10) = 180

Now we can solve for x:

22x - 2 = 180
22x = 182
x = 8.27

To find the measure of angle 2, we substitute the value of x back into the expression for angle 2:

Angle 2 = 10x + 8 = 10(8.27) + 8 = 82.7 + 8 = 90.7

So, the measure of angle 2 is approximately 90.7 degrees. Therefore, the correct answer is 82.