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# In parallelogram PQRS, angle P is four times angle Q. What is the meas

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Joined: 02 Sep 2009
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In parallelogram PQRS, angle P is four times angle Q. What is the meas  [#permalink]

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08 Mar 2018, 02:23
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In parallelogram PQRS, angle P is four times angle Q. What is the measure in degrees of angle P ?

(A) 36

(B) 72

(C) 125

(D) 144

(E) 150

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Joined: 02 Sep 2009
Posts: 49448
Re: In parallelogram PQRS, angle P is four times angle Q. What is the meas  [#permalink]

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08 Mar 2018, 02:24
Bunuel wrote:
In parallelogram PQRS, angle P is four times angle Q. What is the measure in degrees of angle P ?

(A) 36

(B) 72

(C) 125

(D) 144

(E) 150

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Re: In parallelogram PQRS, angle P is four times angle Q. What is the meas  [#permalink]

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08 Mar 2018, 05:41
Bunuel wrote:
In parallelogram PQRS, angle P is four times angle Q. What is the measure in degrees of angle P ?

(A) 36

(B) 72

(C) 125

(D) 144

(E) 150

PROPERTY: Sum of the two adjacent angles in a parallelogram = 180º

angle p = 4* angle q

and p+q = 180

so 4q+q = 180

i.e q = 36º
and p = 4*36 = 144º

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Re: In parallelogram PQRS, angle P is four times angle Q. What is the meas  [#permalink]

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08 Mar 2018, 05:43
Bunuel wrote:
In parallelogram PQRS, angle P is four times angle Q. What is the measure in degrees of angle P ?

(A) 36

(B) 72

(C) 125

(D) 144

(E) 150

In a parallelogram, the consecutive angles are supplementary
i.e. In Parallelogram PQRS, P + Q = 180

Let angle Q be x.
As P is 4 times angle Q, angle P = 4x

Substituting the values of P and Q, $$4x + x = 5x = 180$$ ->$$x = \frac{180}{5} = 36$$

Therefore, the measure of angle P is $$4x$$ = 144 (Option D)
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Re: In parallelogram PQRS, angle P is four times angle Q. What is the meas  [#permalink]

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12 Mar 2018, 09:57
Bunuel wrote:
In parallelogram PQRS, angle P is four times angle Q. What is the measure in degrees of angle P ?

(A) 36

(B) 72

(C) 125

(D) 144

(E) 150

We may recall that consecutive angles of a parallelogram sum to 180; thus:

4n + n = 180

5n = 180

n = 36

So angle P is 4 x 36 = 144 degrees.

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Re: In parallelogram PQRS, angle P is four times angle Q. What is the meas &nbs [#permalink] 12 Mar 2018, 09:57
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