Two adjacent angles form a resulting angle with measure 160° . m<1 = 3x° and m<2=(2x + 10)° solve for x. what are the two unknown angles measures? m<1= ° ,m<2=
Since the two adjacent angles form a resulting angle of 160°, the sum of the measures of the two adjacent angles is 160°.
Therefore, the equation can be set up as:
m<1 + m<2 = 160°
Plugging in the given values for m<1 and m<2:
3x + (2x + 10) = 160°
Combining like terms:
5x + 10 = 160°
Subtracting 10 from both sides:
5x = 150°
Dividing both sides by 5:
x = 30°
To find the measure of angle m<1, plug x=30 into 3x:
m<1 = 3(30) = 90°
To find the measure of angle m<2, plug x=30 into 2x + 10:
m<2 = 2(30) + 10 = 60 + 10 = 70°
Therefore, m<1 = 90° and m<2 = 70°.