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
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.
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
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.
To find the measure of angle 2, we need to remember that angles 1 and 3 are opposite angles and are congruent. This means that they have the same measure.
Given that the measure of angle 1 is (10x + 8) degrees and the measure of angle 3 is (12x - 10) degrees, we can set up the equation:
10x + 8 = 12x - 10
Now we can solve for x:
10x + 10x = 8 + 10
20x = 18
x = 18/20
x = 9/10
Now that we have the value of x, we can substitute it into the measure of angle 1 to find its measure:
Measure of angle 1 = 10x + 8
= 10(9/10) + 8
= 9 + 8
= 17 degrees
Since angle 2 is opposite angle 1, they have the same measure. Therefore, the measure of angle 2 is also 17 degrees.
So, the correct answer is 17.