ANGLE A AND B ARE SUPPLEMENTARY. THE MEASURE OF ANGLE A IS 5X+12 AND THE MEASURE OF ANGLE B IS 6X-30. FIND THE MEASURMENT OF EACH.
5x + 12 + 6x - 30 = 180
11x - 18 = 180
11x = 198
x = 18
Angle A:
(5 * 18) + 12
90 + 12 = 102 degrees
Angle B: ??
supplementary angles add up to 180°
so ...
5x + 12 + 6x - 30 = 180
continue ....
To find the measure of angles A and B, we need to set up an equation based on the information given.
First, let's write down the given information:
- The measure of angle A is 5x + 12.
- The measure of angle B is 6x - 30.
- Angles A and B are supplementary, which means their measures add up to 180 degrees.
Since angles A and B are supplementary, we can write the equation:
(Angle A) + (Angle B) = 180 degrees
Substituting the given measures of angles A and B into the equation, we have:
(5x + 12) + (6x - 30) = 180
Simplifying the equation, we combine like terms:
5x + 12 + 6x - 30 = 180
11x - 18 = 180
Next, we solve the equation to find the value of x:
11x = 180 + 18
11x = 198
x = 198 / 11
x ≈ 18
Now that we have the value of x, we can substitute it back into the expressions for angles A and B to find their measures:
Angle A = 5x + 12 = 5(18) + 12 = 90 + 12 = 102 degrees
Angle B = 6x - 30 = 6(18) - 30 = 108 - 30 = 78 degrees
Therefore, Angle A measures 102 degrees and Angle B measures 78 degrees.