Two adjacent angles, <1 and 42, form a resulting angle that measures 148°
If m <1 = (2x + 8)° and m <2 = (3x), what are the two unknown angle measure?
The sum of the measures of two adjacent angles is equal to the measure of the resulting angle. In this case, the measure of angle 1 plus the measure of angle 2 equals 148°.
Let's set up the equation using the given angle measures:
(2x + 8) + (3x) = 148
Combine like terms:
5x + 8 = 148
Subtract 8 from both sides:
5x = 140
Divide both sides by 5:
x = 28
Now we can find the measure of angle 1 and angle 2 using x = 28:
m<1 = (2x + 8)°
m<1 = (2(28) + 8)°
m<1 = 64°
m<2 = (3x)°
m<2 = (3(28))°
m<2 = 84°
So the measure of angle 1 is 64° and the measure of angle 2 is 84°.