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26 Nov 2010, 13:11
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D
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Difficulty:
15%
(low)
Question Stats:
81% (01:38) correct
19%
(01:54)
wrong
based on 263
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In triangle PQR, the measure of angle P is 30° more than twice the measure of angle Q. What is the measure of angle R?
(1) PQ = QR
(2) The measure of angle P is 78°.
(1) PQ = QR
(2) The measure of angle P is 78°.
26 Nov 2010, 13:38
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rite2deepti
Given: \(\angle{P}=2*\angle{Q}+30\). Question: \(\angle{R}=?\).
Now, as the sum of the angles in a triangle equals to 180 degrees then: \(\angle{P}+\angle{Q}+\angle{R}=180\) --> \(\angle{R}=180-(\angle{P}+\angle{Q})=180-(2*\angle{Q}+30+\angle{Q})=150-3*\angle{Q}\) or \(\angle{R}=150-3*\frac{\angle{P}-30}{2}\). So, knowing the measure of \(\angle{P}\) ( or \(\angle{Q}\)) is sufficient to answer the question.
(1) PQ = QR --> triangle PQR is isosceles (base is PR) --> so \(\angle{R}=\angle{P}\). We also know that \(\angle{R}=150-3*\frac{\angle{P}-30}{2}\) so we have two distinct linear equations with two unknowns and we can solve for them. Sufficient.
(2) The measure of angle P is 78 --> so \(\angle{P}=78\) then we can solve \(\angle{R}=150-3*\frac{\angle{P}-30}{2}\) for \(\angle{R}\). Sufficient.
Answer: D.
For more on this issues check Triangles chapter of Math Book: math-triangles-87197.html
Hope it helps.
27 Nov 2010, 13:11
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rite2deepti
The best thing to do in geometry questions is to make a diagram:
Attachment:
Ques1.jpg [ 7.12 KiB | Viewed 30706 times ]
I have got all angles in terms of angle Q.
angle R = 180 - Q - (30 + 2Q) = 150 - 3Q
(Since sum of all angles in a triangle is 180).
To find angle R, I only need angle Q.
Stmnt 1: If PQ = QR, angle P = angle R.
30 + 2Q = 150 - 3Q. you will get Q and hence the value of angle R.
Stemnt 2: If angle P is 78, 30 + 2Q = 78. You will get value of angle Q and hence value of angle R.
Both statements alone sufficient so answer is D.
