Question

identify two statements that contradict each other.
i. ∠m is an obtuse angle.
ii. m∠m + m∠p = 90°
iii. 180° - m∠m = 25°
iv. m∠p = 120°
a. i and ii
b. i and iv
c. i and iii
d. iii and iv

Explanation:

Step1: Recall angle - type definitions

An obtuse angle has a measure greater than 90° and less than 180°.

Step2: Analyze statement I

Statement I says $\angle M$ is an obtuse angle, so $90^{\circ}

Step3: Analyze statement II

Statement II is $m\angle M + m\angle P=90^{\circ}$. If $m\angle M + m\angle P = 90^{\circ}$, then $m\angle M<90^{\circ}$ (since $m\angle P\geq0^{\circ}$), which contradicts the fact that $\angle M$ is obtuse from statement I.

Step4: Analyze statement III

From $180^{\circ}-m\angle M = 25^{\circ}$, we can solve for $m\angle M$: $m\angle M=180^{\circ}- 25^{\circ}=155^{\circ}$, which is consistent with $\angle M$ being obtuse.

Step5: Analyze statement IV

Statement IV is $m\angle P = 120^{\circ}$. It has no direct contradiction with $\angle M$ being obtuse.

Answer:

A. I and II