Question

identify two statements that contradict each other.
i. $angle m$ is an obtuse angle.
ii. $mangle m + mangle p=90^{circ}$
iii. $180^{circ}-mangle m = 25^{circ}$
iv. $mangle p = 120^{circ}$
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 says $m\angle M + m\angle P=90^{\circ}$. If $\angle M$ is obtuse ($m\angle M>90^{\circ}$), then $m\angle M + m\angle P>90^{\circ}$, which contradicts statement II.

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 says $m\angle P = 120^{\circ}$. From statement II $m\angle M + m\angle P=90^{\circ}$, if $m\angle P = 120^{\circ}$, then $m\angle M+120^{\circ}=90^{\circ}$, so $m\angle M=- 30^{\circ}$, which is not possible for an angle measure. But the main contradiction is between I and II.

Answer:

A. I and II