Question

<1 and <2 are supplementary angles. m <1 is 4y+7, and m<2 is 9y+4. Find m<2.

Answer 1

Okay, so supplementary angles = 180 degrees.

Starting equation : 4y + 7 + 9y + 4 = 180

Combine like terms : 13y + 11 = 180

Subtract 11 from both sides : 13y = 169

Divide 13 from both sides : y = 13

Insert y value into original m<2 equation : 9(13) + 4

Solve : 121 degrees

If you want to check your work, all you have to do is insert y value into original m<1 equation and then add both m<1 and m<2. If they equal 180, your answer is correct.

4(13) + 7 = 59

59 + 121 = 180

Answer 2

Supplementary angles are angles that add to 180°. Given that $\angle 1$ and $\angle 2$ are supplementary angles, we can say that the measures of the two angles add to 180°, as shown below:

$m \angle 1 + m \angle 2 = 180$

The problem also gave us values for $m \angle 1$ and $m \angle 2$, which we can substitute into the equation we found in the last step, as shown below:

$(4y + 7) + (9y + 4) = 180$

$13y + 11 = 180$

$13y= 169$

$y = 13$

We have found that y = 13. We can use this to find $m \angle 2$ by "plugging in" the 13 for y:

$m \angle 2 = 9y + 4$

$m \angle 2 = 9(13) + 4$

$m \angle 2 = 121$

The measure of angle 2, $m \angle 2$ is 121°.