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In triangle PQR, the measure of angle P is 30° greater than twice the
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22 Feb 2024, 01:49
22 Feb 2024, 01:49
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In triangle PQR, the measure of angle P is 30° greater than twice the measure of angle Q. If PQ = QR, what is the measure of angle R?
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78
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Re: In triangle PQR, the measure of angle P is 30° greater than twice the
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22 Feb 2024, 12:05
22 Feb 2024, 12:05
1
We're given that 2 sides of the triangle are equal, but one of its angles, Q, is different from the other angles. Therefore, PQR is an isosceles triangle and the measures of angles P and R are equal. (The two angles opposite from the two equal sides of an isosceles triangle are equal.)
Since the measure of angle P is 30° greater than twice the measure of angle Q:
P = 30+2Q = R
The interior angles of a triangle always add up to 180°:
P + Q + R = 180
(30+2Q) + Q + (30+2Q) = 180
5Q + 60 = 180
Q = 24
Solve for R:
30 + 2(Q) = 30 + 2(24) = 78
trianglePQR.png [ 19.02 KiB | Viewed 517 times ]
Since the measure of angle P is 30° greater than twice the measure of angle Q:
P = 30+2Q = R
The interior angles of a triangle always add up to 180°:
P + Q + R = 180
(30+2Q) + Q + (30+2Q) = 180
5Q + 60 = 180
Q = 24
Solve for R:
30 + 2(Q) = 30 + 2(24) = 78
Attachment:
trianglePQR.png [ 19.02 KiB | Viewed 517 times ]
gmatclubot
Re: In triangle PQR, the measure of angle P is 30° greater than twice the [#permalink]
22 Feb 2024, 12:05
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