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The figure shows parallelogram ABCD where AB = 6, AD = y,

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The figure shows parallelogram ABCD where AB = 6, AD = y,

by Max@Math Revolution » Wed Feb 05, 2020 11:41 pm
[GMAT math practice question]

The figure shows parallelogram ABCD where AB = 6, AD = y, ∠ABC = 70 and ∠ACD = 85. If the perimeter of ABCD is 28 what is the value of x + y?
2.6PS.png
A. 31
B. 33
C. 35
D. 37
E. 39
Last edited by Max@Math Revolution on Mon Feb 10, 2020 12:55 am, edited 2 times in total.
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Re: The figure shows parallelogram ABCD where AB = 6, AD = y, ∠ABC = 70o and ∠ACD = 85. If the perimeter of ABCD is 28

by jbryant62 » Thu Feb 06, 2020 7:51 am
Max@Math Revolution wrote: ↑
Wed Feb 05, 2020 11:41 pm
 [GMAT math practice question]

The figure shows parallelogram ABCD where AB = 6, AD = y, ∠ABC = 70o and ∠ACD = 85. If the perimeter of ABCD is 28 what is the value of x + y?

2.6PS.png

A. 31
B. 33
C. 35
D. 37
E. 39
opposite angles of a parallelogram are equal. Therefore angle ADC is equal to 70. The angles of a triangle equal 180. 70+85=155. 180-155=25. X=25.

Opposite sides are equal to each other. AB =6, therefore CD equal 6. Perimeter equals 28. 28-12=16 Divide by the two sides. 16/2=8

25+8=33.
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Re: The figure shows parallelogram ABCD where AB = 6, AD = y,

by Max@Math Revolution » Mon Feb 10, 2020 12:55 am
=>

Since the perimeter of ABCD is 28, we have 2(6 + y) = 28, 12 + 6y = 28, 6y = 16 or y = 8.
We have x = 180 – (70 + 85) = 25.
Thus, x + y = 25 + 8 = 33.

Therefore, B is the answer.
Answer: B
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