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

[BTGmoderatorDC]

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

[swerve]

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

[Scott@TargetTestPrep]

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