Two adjacent angles, ∠1 and ∠2, form a resulting angle that measures 135°
°
. If m∠1 = (2x)°
°
and m∠2 = (2x + 7)°
°
, what are the two unknown angle measures?
m∠1 = Response area°
°
m∠2 = Response area°
m∠1 = (2x)°
m∠2 = (2x + 7)°
To find the unknown angle measures, we need to set up an equation based on the given information.
According to the problem, the resulting angle formed by ∠1 and ∠2 measures 135°. This can be expressed as:
m∠1 + m∠2 = 135
Substituting the values of m∠1 and m∠2 in terms of x:
(2x) + (2x + 7) = 135
Simplifying the equation:
4x + 7 = 135
Subtracting 7 from both sides:
4x = 128
Dividing both sides by 4:
x = 32
Now we can find the values of m∠1 and m∠2 by substituting x = 32 into the given expressions:
m∠1 = (2x)° = (2 * 32)° = 64°
m∠2 = (2x + 7)° = (2 * 32 + 7)° = 71°
Therefore, the two unknown angle measures are:
m∠1 = 64°
m∠2 = 71°