Chapter 2.6, Problem 1ST2

To determine

To write :The name of one possible measure of $\angle HOK$ .

Answer to Problem 1ST2

The possible measure of

  $\overline{XD}\perp \overline{XF}$

Explanation of Solution

Given information:

The angle $\angle HOK$ has a supplement, but can't have a complement.

Consider the statement below and state the definition, postulate, property or theorem that justifies the conclusion

The angle $\angle HOK$ has a supplement but can not have a complement.

From Definition of Supplementary angles,

Supplements are two angles whose measures have the sum ${180}^{\circ }$

From Definition of Complementary angles,

Complements are two angles whose measures have the sum ${90}^{\circ }$

Therefore, from above argument

The $\angle HOK$ angle should be greater than ${90}^{\circ }$ and lesser than ${180}^{\circ }$ .

Therefore, the possible measure of $\angle HOK={120}^{\circ }$

Hence, the answer is $\angle HOK={120}^{\circ }$