Angle x is (2n + 12)°, and angle y is (3n + 18)° . Find the measure of angle x.
Note: not drawn to scale.
Responses
A 30°30°
B 108°108°
C 24°24°
D 72°72°
E 180°
Since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:
x + y + 90° = 180°
Substituting in (2n + 12)° for x and (3n + 18)° for y, we get:
(2n + 12)° + (3n + 18)° + 90° = 180°
Simplifying and solving for n, we get:
5n + 120° = 180°
5n = 60°
n = 12
Now we can substitute n = 12 back into our expressions for x and y to get their measures:
x = (2n + 12)° = (2(12) + 12)° = 36°
y = (3n + 18)° = (3(12) + 18)° = 54°
Therefore, the measure of angle x is 36°, which is answer choice D.