Question

Look at the angles below. Which is not a true statement about the angles?

Answer 1

To solve the exercise, let us analyze the answer options:

Option A.

A straight angle is an angle whose sides line in opposite directions from the vertex in the same straight line.

As we can see in the graph, the angle KJL is straight. Therefore, the measure of angle KJL is 180°.

Therefore, the statement is true.

Option B.

The angles KJM and MJL are supplementary, that is, angles add up to 180°.

Then, we can write and solve for x, the following equation:

`\begin{gathered} 112\text{\degree}+(3x+50)\text{\degree}=180\text{\degree} \\ 112\text{\degree}+(3x)\text{\degree}+50\text{\degree}=180\text{\degree} \\ \text{ Add similar terms} \\ 162\text{\degree}+(3x)\text{\degree}=180\text{\degree} \\ \text{ Subtract 162\degree{}from both sides of the equation} \\ 162\text{\degree}+(3x)\text{\degree}-162\text{\degree}=180\text{\degree}-162\text{\degree} \\ (3x)\text{\degree}=18\text{\degree} \\ \text{ Divide by 3\degree from both sides of the equation} \\ \frac{(3x)\text{\degree}}{3\text{\degree}}=\frac{18\text{\degree}}{3\text{\degree}} \\ $$\boldsymbol{x=6}$$ \end{gathered}`

Therefore, the statement is true.

Option C.

The angles HJK and MJL are vertical, that is, opposite angles made by intersecting lines. Vertical angles are congruent, that is, they have the same measure.

In this case, we have:

`m\angle HJK=m\angle MJL`

Then, to find the measure of angle HJK, we replace x = 6 in the equation of the angle MJL:

`\begin{gathered} m\angle HJK=m\angle MJL \\ m\angle HJK=(3x+50)\text{\degree} \\ m\angle HJK=(3\cdot6+50)\text{\degree} \\ m\angle HJK=(18+50)\text{\degree} \\ m\angle HJK=68\text{\degree} \end{gathered}`

Therefore, the statement is not true.

Option D.

The angles KJM and HJL also are vertical. Then, these angles are also congruent.

`\begin{gathered} m\angle KJM=m\angle HJL \\ 112\text{\degree}=m\angle HJL \end{gathered}`

Thus, this statement is true.

Therefore, the statement that is not true about the angles is the one shown in option C.