Question

determine whether each statement can or cannot be assumed from the figure. 1. ∠mtr and ∠ntp are vertical angles. select choice 2. ∠ntp and ∠ptr are supplementary. select choice 3. ∠qtr≅∠ptm select choice 4. ∠qtp is a right angle. select choice

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 formed by the intersection of lines $MP$ and $RN$, so they are vertical angles.

Step2: Recall supplementary - angle definition

Supplementary angles add up to 180 degrees. $\angle NTP$ and $\angle PTR$ form a linear pair (a straight - line angle which is 180 degrees), so they are supplementary.

Step3: Analyze angle congruence

There is no information in the figure to suggest that $\angle QTR\cong\angle PTM$. Just because they are angles formed by intersecting lines does not mean they are congruent without further information like equal arc measures (in a circle context) or given angle - measure equalities.

Step4: Analyze right - angle condition

There is no right - angle symbol in the figure to indicate that $\angle QTP$ is a right angle. So we cannot assume it is a right angle.

Answer:

1. Can be assumed
2. Can be assumed
3. Cannot be assumed
4. Cannot be assumed