Final answer:
To find the measure of angle SPQ, we need to understand what a linear pair is and use the equation for a linear pair. By substituting the given values and simplifying the equation, we can find the value of x. Substituting the value of x into the expression for m∠SPQ gives us the measure of angle SPQ, which is 87°.
Step-by-step explanation:
To find the measure of angle SPQ, we first need to understand what a linear pair is. A linear pair of angles is formed when two angles are adjacent (share a common side) and their non-shared sides form a straight line.
Given that ∠RPS and ∠SPQ form a linear pair, we have the equation:
m∠RPS + m∠SPQ = 180°
Substituting the given values into the equation, we have:
(2x+1) + (2x-5) = 180°
Simplifying the equation, we get:
4x - 4 = 180°
Adding 4 to both sides, we have:
4x = 184°
Dividing both sides by 4, we find that:
x = 46°
Now, we can substitute the value of x into the expression for m∠SPQ:
m∠SPQ = 2x - 5 = 2(46°) - 5 = 92° - 5 = 87°
Therefore, m∠SPQ is 87°.