A Cute Angle

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Nov 04, 2014 1:58 am

The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram?
A. 90°
B. 75°
C. 60°
D. 45°
E. 30°

Made Up!

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Source: Beat The GMAT — Problem Solving | Tue Nov 04, 2014 1:58 am

chetan86: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Sun Mar 31, 2013 9:14 am; Thanked: 2 times

by chetan86 » Tue Nov 04, 2014 7:42 am

sanju09 wrote:The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram?
A. 90°
B. 75°
C. 60°
D. 45°
E. 30°

Made Up!

In Parallelogram adjacent angles make 180°, while opposite angles are equal.
so, x+x+90°=180°
Ans: D. 45°

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Wed Nov 05, 2014 3:14 am

Let's use for convenience a parallelogram with a horizontal base and one obtuse angle directly above (vertically) the opposite acute angle. Now draw a line between these 2 angles to create 2 right angle triangles.
Each triangle will be isosceles, so the acute angle will be 90/2 - 45 degrees.

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