An obtuse LG HI has a measure of 135°. It contains adjacent angles GHJ and JHI.

Question

ZGH J has a measure of 112°. What is the measure of LJHI? (1 point)
O 68°
O 15°
O 90°
O 23°

Answer 1

To find the measure of LJHI, we can subtract the sum of the measures of ZGHJ and JHI from the measure of an obtuse angle, which is 135°.

First, the measure of ZGHJ is given as 112°.

Next, let's find the measure of JHI. The sum of the measures of ZGHJ and JHI is equal to the measure of GHJ. Therefore, GHJ must have a measure of 135° - 112° = 23°.

Since JHI is an adjacent angle to GHJ, it must have the same measure as GHJ, which is 23°.

Finally, to find the measure of LJHI, we subtract the sum of ZGHJ and JHI from the measure of the obtuse angle, 135° - (112° + 23°) = 135° - 135° = 0°.

Therefore, the measure of LJHI is 0°.