For question 11, find the measure of angle ABC.

Solution:

We are given a triangle ABC. The angle at C is a right angle, indicated by the square symbol. Therefore, angle ACB = 90 degrees.

We are given that angle DAB is a straight line, and angle CAD is an exterior angle to triangle ABC at vertex A. The measure of angle CAD is given as 150 degrees.

Since angle CAB and angle CAD form a straight line, they are supplementary angles.

Angle CAB + Angle CAD = 180 degrees

Angle CAB + 150 degrees = 180 degrees

Angle CAB = 180 degrees - 150 degrees = 30 degrees.

Now we have two angles in triangle ABC: angle ACB = 90 degrees and angle CAB = 30 degrees.

The sum of angles in a triangle is 180 degrees.

Angle ABC + Angle BCA + Angle CAB = 180 degrees

Angle ABC + 90 degrees + 30 degrees = 180 degrees

Angle ABC + 120 degrees = 180 degrees

Angle ABC = 180 degrees - 120 degrees = 60 degrees.

Answer: 60 degrees