4. P lies in the interior of ∠RST. m∠RSP = 40° and m∠TSP = 10°. m∠RST = ? (4 pts)
who was talking about a triangle?
If P lies in the interior of ∠RST, then
m∠RST = m∠RSP + m∠TSP = 40+10 = 50°
You are correct, my previous response was incorrect.
If P lies in the interior of ∠RST, then we can find the measure of angle RST by adding the measures of angles RSP and TSP:
m∠RST = m∠RSP + m∠TSP = 40° + 10° = 50°.
Therefore, m∠RST = 50°.
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Apologies for the confusion in my previous response. The correct answer is indeed m∠RST = 50°. Thank you for pointing out the mistake.
To find the measure of ∠RST, we can use the fact that the sum of the angles in a triangle is 180 degrees.
First, let's consider the triangle ∆RST. We are given that ∠RSP measures 40° and ∠TSP measures 10°.
To find the measure of ∠RST, we can subtract the measured angles from 180°.
∠RST = 180° - (m∠RSP + m∠TSP)
∠RST = 180° - (40° + 10°)
∠RST = 180° - 50°
∠RST = 130°
Therefore, the measure of ∠RST is 130°.
To find the measure of angle RST, we can use the fact that the sum of the angles in a triangle is 180°.
We know that m∠RSP = 40° and m∠TSP = 10°, so we can find the measure of angle RPT:
m∠RPT = 180° - m∠RSP - m∠TSP
m∠RPT = 180° - 40° - 10°
m∠RPT = 130°
Since P lies in the interior of ∠RST, angles RPT and RST are adjacent angles. The sum of these two angles is 180°. So, we can find the measure of angle RST:
m∠RST = 180° - m∠RPT
m∠RST = 180° - 130°
m∠RST = 50°
Therefore, m∠RST = 50°.