The measures of the three interior angles of are in the ratio 2:3:7. What type of triangle is ?
A) acute
B) right
C) obtuse
D) isosceles

Question

The measures of the three interior angles of  are in the ratio 2:3:7. What type of triangle is  ?
A) acute 
B) right 
C) obtuse 
D) isosceles

Quizplus · Accepted Answer

Let the three angles be 2x, 3x, and 7x.
The sum of the interior angles of a triangle is 180 degrees, so we have:

2x + 3x + 7x = 180
12x = 180
x = 15

Thus, the three angles are:

2x = 30 degrees
3x = 45 degrees
7x = 105 degrees

Since the largest angle is greater than 90 degrees, the triangle is obtuse.

The Measures of the Three Interior Angles of Are