5. QS bisects ∠PQR. If m∠PQS = 3x and m∠RQS = 2x + 6, then m∠PQR = ? (4 pts)
Since QS bisects ∠PQR, we can set up the equation:
m∠PQS + m∠RQS = m∠PQR
3x + 2x + 6 = m∠PQR
5x + 6 = m∠PQR
Therefore, m∠PQR = 5x + 6.
but we want a numeric value. Since QS bisects ∠PQR,
m∠PQS = m∠RQS
3x = 2x+6
x = 6
Now we know that m∠PQR = 5x+6 = 36
so m∠PQR = 36°
You are correct. Based on the given information and the fact that QS bisects ∠PQR, we can set up the equation 3x = 2x + 6. Solving for x, we find that x = 6.
Substituting this value back into the expression for m∠PQR, we get 5x + 6 = 5(6) + 6 = 30 + 6 = 36.
Therefore, m∠PQR = 36°.
To find the measure of ∠PQR, we need to use the properties of angle bisectors.
First, let's set up an equation based on the given information. We know that ∠PQS + ∠RQS = ∠PQR because QS bisects ∠PQR.
So, we can write the equation as:
m∠PQS + m∠RQS = m∠PQR
Substituting the given measures, we have:
3x + (2x + 6) = m∠PQR
Simplifying the equation, we combine like terms:
5x + 6 = m∠PQR
Therefore, the measure of ∠PQR is 5x + 6.