In triangle ABC, side AB is perpendicular to side BC. If angle CAB is greater than 45 degrees, then which of the

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Nov 22, 2020 4:49 pm

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In triangle ABC, side AB is perpendicular to side BC. If angle CAB is greater than 45 degrees, then which of the following could be the value of angle ACB?

A. 75°
B. 65°
C. 55°
D. 45°
E. 35°

OA E

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sun Nov 22, 2020 4:49 pm

swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: In triangle ABC, side AB is perpendicular to side BC. If angle CAB is greater than 45 degrees, then which of the

by swerve » Mon Nov 23, 2020 12:34 pm

BTGmoderatorDC wrote: ↑
Sun Nov 22, 2020 4:49 pm
In triangle ABC, side AB is perpendicular to side BC. If angle CAB is greater than 45 degrees, then which of the following could be the value of angle ACB?

A. 75°
B. 65°
C. 55°
D. 45°
E. 35°

OA E

Source: Magoosh

Triangle $ADC$

Angle $D = 90$ and angle $ACB = 45$

So, $45+90+ \text{angle } DAC= 180$

Angle $DAC = 55$

So, angel $ACB = 35 \Longrightarrow$ E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8176; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In triangle ABC, side AB is perpendicular to side BC. If angle CAB is greater than 45 degrees, then which of the

by Scott@TargetTestPrep » Mon Nov 30, 2020 10:46 am

BTGmoderatorDC wrote: ↑
Sun Nov 22, 2020 4:49 pm
In triangle ABC, side AB is perpendicular to side BC. If angle CAB is greater than 45 degrees, then which of the following could be the value of angle ACB?

A. 75°
B. 65°
C. 55°
D. 45°
E. 35°

OA E

Solution:

Since AB is perpendicular to B, we see that triangle ABC is a right triangle with right angle at B. Therefore, angle ABC = 90 degrees. Since angle CAB is greater than 45 degrees, the third angle, angle ACB, must be less than 45 degrees. Thus, angle ACB could be 35 degrees.

Answer: E

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