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

In a triangle, the sum of the three interior angles is always 180 degrees. Let the measures of the angles be 2x, 3x, and 7x. Then we have 2x + 3x + 7x = 180, which simplifies to 12x = 180, or x = 15. This means the angles are 30 degrees, 45 degrees, and 105 degrees, which shows that the triangle is obtuse (an obtuse triangle has one angle greater than 90 degrees). Therefore, the answer is C, obtuse.

The Measures of the Three Interior Angles of Are