Given the right triangle, let's find the following measures:
m∠ABC, m∠ACB, m∠CAB
• 1. ,m∠ABC = 28°
From the tiangle, we can see the measure of angle ABC is given as 28 degrees
• 2. ,m∠ACB = 90°
A right triangle has one angle that measures 90 degrees.
The angle that connects both legs in a right triangle is 90 degrees
Therefore, the measure of angle ACB is 90 degrees.
• 3. m∠CAB
To find the measure of angle CAB, apply the Triangle Angle Sum theorem which states that the sum of interior angles in a triangle is 180 degrees.
Thus, we have:
m∠ABC + m∠ACB + m∠CAB = 180
28 + 90 + m∠CAB = 180
118 + m∠CAB = 180
Subtract 118 from both sides:
118 - 118 + m∠CAB = 180 - 118
m∠CAB = 62°
ANSWER:
m∠ABC = 28°
m∠ACB = 90°
m∠CAB = 62°