Question

determine whether each statement can or cannot be assumed from the figure.

1. ∠mtr and ∠ntp are vertical angles
2. ∠ntp and ∠ptr are supplementary.
3. ∠qtr≅∠ptm
4. ∠qtp is a right angle.

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed by two intersecting lines and are opposite each other. $\angle MTR$ and $\angle NTP$ are opposite angles formed by the intersection of two lines at point $T$, so they are vertical angles and this can be assumed.

Step2: Recall supplementary - angle definition

Supplementary angles add up to 180 degrees. Just from the figure, without any right - angle or other angle - measure indicators, we cannot assume that $\angle NTP$ and $\angle PTR$ are supplementary.

Step3: Recall angle - congruence criteria

There is no indication in the figure (such as equal - angle markings, parallel lines etc.) to suggest that $\angle QTR\cong\angle PTM$, so this cannot be assumed.

Step4: Recall right - angle definition

There is no right - angle symbol at $\angle QTP$, so we cannot assume that it is a right angle.

Answer:

1. can be assumed
2. cannot be assumed
3. cannot be assumed
4. cannot be assumed