Question

if ( mangle nsm = 98^{circ} ), then what is ( mangle msp )?
answer attempt 1 out of 3
( mangle msp=) 。 submit answer

Explanation:

Step1: Find the measure of ∠2

Since ∠1 and ∠2 are supplementary (they form a linear - pair), and ∠1 and ∠NSM are vertical angles (∠1 = ∠NSM = 98°).
Using the linear - pair property: ∠1+∠2 = 180°.
Substitute ∠1 = 98° into the equation: 98°+∠2 = 180°.
Solve for ∠2: ∠2=180° - 98° = 82°.

Step2: Use the corresponding angles property

∠2 and ∠MSP are corresponding angles.
By the corresponding angles postulate (if two parallel lines are cut by a transversal, then corresponding angles are equal). Here, assuming the lines are parallel (as per the angle - relationship context in such problems), ∠MSP = ∠2.

Answer:

82