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 between 90° and 180°.

Step2: Analyze statement I

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

Step3: Analyze statement II

Statement II is \(m\angle M + m\angle P=90^{\circ}\), which implies \(m\angle M=90^{\circ}-m\angle P\), so \(m\angle M < 90^{\circ}\). This contradicts statement I.

Step4: Analyze statement III

From \(180^{\circ}-m\angle M = 25^{\circ}\), we can solve for \(m\angle M\):
\[

$$\begin{align*} 180^{\circ}-m\angle M&=25^{\circ}\\ m\angle M&=180^{\circ}- 25^{\circ}\\ m\angle M&=155^{\circ} \end{align*}$$

\]
This is consistent with ∠M being an obtuse - angle.

Step5: Analyze statement IV

Statement IV says \(m\angle P = 120^{\circ}\), which contradicts statement II (\(m\angle M + m\angle P=90^{\circ}\)) but we are looking for a contradiction with statement I.

Answer:

A. I and II