Two adjacent angles <1 and <2 form a resulting angle with measures 135 if m<1=(2x) and m<2=(2x+7) what are the two unknown measures?

Answer 1

Let's call the measure of angle 1, $m<1$, as $2x$.

The measure of angle 2, $m<2$, is given as $2x+7$.

The resulting angle formed by angles 1 and 2 is said to measure $135^\circ$.

Therefore, we can set up the equation:

$2x + 2x + 7 = 135$

Simplifying:

$4x + 7 = 135$

Subtracting 7 from both sides:

$4x = 128$

Now, divide by 4:

$x = 32$

So, the measure of angle 1, $m<1$, is $2x = 2(32) = 64^\circ$.

The measure of angle 2, $m<2$, is $2x + 7 = 2(32) + 7 = 71^\circ$.

Therefore, the two unknown measures are $m<1 = 64^\circ$ and $m<2 = 71^\circ$.