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# Two consecutive angles of a parallelogram have angle measures, in degr

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Joined: 02 Sep 2009
Posts: 52161
Two consecutive angles of a parallelogram have angle measures, in degr  [#permalink]

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26 Apr 2018, 12:33
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15% (low)

Question Stats:

83% (01:12) correct 17% (01:26) wrong based on 58 sessions

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Two consecutive angles of a parallelogram have angle measures, in degrees, of 2x - 30 and x + 60. What is the measure, in degrees, of the smaller angle?

(A) 50
(B) 60
(C) 70
(D) 100
(E) 110

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Re: Two consecutive angles of a parallelogram have angle measures, in degr  [#permalink]

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26 Apr 2018, 14:06
Bunuel wrote:
Two consecutive angles of a parallelogram have angle measures, in degrees, of 2x - 30 and x + 60. What is the measure, in degrees, of the smaller angle?

(A) 50
(B) 60
(C) 70
(D) 100
(E) 110

Two consecutive angles of a parallelogram have angle measures that add up to 180.
Therefore (2x-30) + (x+60) = 180
3x+30 = 180
3x = 150
x= 50

2x-30 = 70

x+60 = 110

Therefore the smaller angle is 70 degrees

Hence C = 70 is the answer.
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Re: Two consecutive angles of a parallelogram have angle measures, in degr  [#permalink]

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26 Apr 2018, 23:14
Bunuel wrote:
Two consecutive angles of a parallelogram have angle measures, in degrees, of 2x - 30 and x + 60. What is the measure, in degrees, of the smaller angle?

(A) 50
(B) 60
(C) 70
(D) 100
(E) 110

Ans: C

we know from theory that in a parallelogram opposite angles are equal and sum of all the interior angles is 360 so
2(2x-30)+2(x+60) = 360
x= 50
by putting this we get two angles = 70 and 110. smaller one is 70
Ans : C
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Re: Two consecutive angles of a parallelogram have angle measures, in degr  [#permalink]

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30 Apr 2018, 15:31
Bunuel wrote:
Two consecutive angles of a parallelogram have angle measures, in degrees, of 2x - 30 and x + 60. What is the measure, in degrees, of the smaller angle?

(A) 50
(B) 60
(C) 70
(D) 100
(E) 110

Two consecutive angles of a parallelogram always sum to 180 degrees; thus:

2x - 30 + x + 60 = 180

3x = 150

x = 50

We see that one angle is 2(50) - 30 = 70 degrees, and the other is 50 + 60 = 110 degrees. So the smaller angle is 70 degrees.

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Re: Two consecutive angles of a parallelogram have angle measures, in degr &nbs [#permalink] 30 Apr 2018, 15:31
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# Two consecutive angles of a parallelogram have angle measures, in degr

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