Find the angles of a triangle if it is known that the measures of the angles are $x , 2 x \text {, and } 6 x$ .
A) $30 ^ { \circ } , 60 ^ { \circ } , 90 ^ { \circ }$
B) $40 ^ { \circ } , 80 ^ { \circ } , 240 ^ { \circ }$
C) $20 ^ { \circ } , 40 ^ { \circ } , 120 ^ { \circ }$
D) $20 ^ { \circ } , 60 ^ { \circ } , 70 ^ { \circ }$
E) $30 ^ { \circ } , 60 ^ { \circ } , 180 ^ { \circ }$

Question

Quizplus · Accepted Answer

The sum of angles in a triangle is 180 degrees.

Therefore, we have:

$$x + 2x + 6x = 180^\circ$$

Simplifying the equation, we get:

$$9x = 180^\circ$$

$$x = 20^\circ$$

Using this value of $x$, we find that the three angles of the triangle are:

$$20^\circ, 40^\circ, 120^\circ$$

Therefore, the answer is choice C.

Find the Angles of a Triangle If It Is Known x,2x, and 6xx , 2 x \text {, and } 6 xx,2x, and 6x

Find the Angles of a Triangle If It Is Known $x , 2 x \text {, and } 6 x$