1. 
Find m∠B
and m∠C. 
Solution:
m∠A + m∠B + m∠C = 180
38 + x + (x + 2) = 180
40 + 2x = 180
2x = 140
x = 70 = m∠B
x + 2 = 72 = m∠C 
2. The angles in a triangle are represented by (4x  6)º, (2x + 1)º and (x + 3)º. Is this a right triangle? 
Solution:
(4x  6) + (2x + 1) + (x + 3) = 180
7x  2 = 180
7x = 182
x = 26
(4x  6)º = 98º
(2x + 1)º = 53º
(x + 3)º = 29º
No. The triangle is obtuse. 
3. 
m∠ABC=m∠BCD
Find m∠ACD. 
Solution: m∠BCD = 56º.
In ΔABC, 85º + 56º + m∠BCA = 180º
m∠BCA = 39º
m∠ACD = 56º  39º = 17º

4. The angles in a triangle are in the ratio of 1 : 2 : 3. Find the measure of the angles in the triangle.
Solution:
x + 2x + 3x = 180
6x = 180
x = 30
The angles are 30º, 60º, and 90º.
