Geometry problems:

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\'manpreet singh: Master | Next Rank: 500 Posts; Posts: 271; Joined: Tue May 22, 2012 3:22 am; Thanked: 7 times; Followed by:3 members

Geometry problems:

by \'manpreet singh » Sat Jul 21, 2012 11:48 pm

Q.1 If a and b are complementary angles (they sum to 90Â°), name three other pairs of complementary angles.see the diagram below (named untitled)

Q.2 A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

Q.3 If g =11y, a = 4x - y, and d = 5y + 2x - 20, find h.Refer to diagram below(untitled 1)

Attachments

: Q.1

: Q.3

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Source: Beat The GMAT — Problem Solving | Sat Jul 21, 2012 11:48 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sun Jul 22, 2012 1:18 am

'manpreet singh wrote:Q.1 If a and b are complementary angles (they sum to 90Â°), name three other pairs of complementary angles.see the diagram below (named untitled)

Using the vertical angle rule (opposite angles of intersecting lines are equal), we know that:

a=d
and
b=e

So, since a and b are complementary, d and e must also be complementary.

Further, since a=d, b and d are complementary; similarly, since b=e, a and e are complementary.

We know that c=f and that those two angles sum to 180 (since the other 4 angles sum to 90+90=180 and the whole circle must sum to 360), but we don't know the actual values of c and f.