Question

If OP bscts Z HOT, OG bscts POT, and mZ HOT = 84, then solve for:

a) m ZHOP =
b) m Z TOG =
c) m Z HOG =

a) 42
b) 42
c) 42
d) None of the above

Answer 1

The measures of the angles ZHOP, ZTOG, and ZHOG, given that lines OP and OG bisect the angles ZHOT and POT, are 42°, 42°, and 84° respectively.

Step-by-step explanation:

The question provided involves solving for angles in a geometry problem. Given that m∠HOT = 84°, and that lines OP and OG bisect angles ZHOT and POT respectively, we need to solve for the measures of angles ZHOP, ZTOG, and ZHOG.

To solve for m∠ZHOP, we divide the measure of angle HOT by 2, as OP is a bisector, getting 42°.

Next, OG bisects angle POT, which is supplementary to HOT since they form a straight line. Therefore, POT also measures 84°, and its bisecting gives us ZTOG as 42°.

Finally, to solve for m∠ZOG, we add the measures of ZHOP and ZTOG since they are adjacent angles sharing the bisector OG, resulting in 84°.