Question

1. which statement(s) cannot be assumed from the figure? a. ∠khj and ∠ghm are complementary b. ∠ghk and ∠jhk are a linear pair c. (overrightarrow{hl}) is perpendicular to (overrightarrow{hj}) d. ∠ghm and ∠mhk are adjacent angles e. (overrightarrow{hl}) is perpendicular to (overrightarrow{hm})

Explanation:

1. Complementary angles add up to 90 degrees. There is no indication in the figure that ∠KHJ and ∠GHM sum to 90 degrees.
2. A linear - pair of angles are adjacent and supplementary. ∠GHK and ∠JHK share a common side and a common vertex and form a straight - line, so they are a linear pair.
3. Perpendicular lines form right angles. There is no right - angle symbol or other indication that $\overrightarrow{HL}$ is perpendicular to $\overrightarrow{HJ}$.
4. Adjacent angles share a common side and a common vertex. ∠GHM and ∠MHK share side $\overrightarrow{HM}$ and vertex H, so they are adjacent angles.
5. There is no right - angle symbol or other indication that $\overrightarrow{HL}$ is perpendicular to $\overrightarrow{HM}$.

Answer:

A. ∠KHJ and ∠GHM are complementary
C. $\overrightarrow{HL}$ is perpendicular to $\overrightarrow{HJ}$
E. $\overrightarrow{HL}$ is perpendicular to $\overrightarrow{HM}$