The difference of the angle measures is 42°.
Given that angle ABC is a right angle (90°) and angle BAC is (3x)°, and angle BCA is (x + 2)° in triangle ABC, we can use the fact that the sum of the angles in a triangle is 180° to solve for x.
90° + (3x)° + (x+2)° = 180°
4x + 92° = 180°
Subtracting 92° from both sides, we get:
4x = 88°
Dividing both sides by 4, we find:
x = 22°
To find the difference of the angle measures, we subtract the smaller from the larger angle:
(x+2)° - (3x)° = 22° + 2° - 66° = -42°
So, the difference of the angle measures is 42°.
The probable question may be:
In triangle ABC , angle ABC=90°, angle BAC=(3x)°, angle BCA=(x + 2)° Solve for x and then find the difference of the angle measures.
(x + 2)°
a) 18°
b) 20°
c) 36°
d) 42°