Two adjacent angles, ∠1
and ∠2
, form a resulting angle with measure 135° . If m∠1=(2x)° and m∠2=(2x+7)° , what are the two unknown angle measures?
To solve this problem, we can set up an equation.
According to the problem, the measure of angle 1, represented as m∠1, is equal to 2x°.
Similarly, the measure of angle 2, represented as m∠2, is equal to (2x + 7)°.
Since the problem states that the resulting angle formed by angles 1 and 2 is 135°, we can write the equation:
m∠1 + m∠2 = 135
Substituting the values of m∠1 and m∠2:
2x + (2x + 7) = 135
Simplifying the equation:
4x + 7 = 135
Next, isolate the variable by subtracting 7 from both sides:
4x = 128
Lastly, solve for x by dividing both sides by 4:
x = 32
Now that we have found the value of x, we can substitute it back into the expressions for m∠1 and m∠2 to find their values.
m∠1 = 2x = 2(32) = 64 degrees
m∠2 = 2x + 7 = 2(32) + 7 = 71 degrees
Therefore, the measures of angles 1 and 2 are 64 degrees and 71 degrees, respectively.