Solve the problem.
-In an isosceles triangle, one angle is 33° greater than the other two angles. Find the measure of all three angles.
A) 57°, 57°, 66°
B) 36.8°, 36.8°, 106.5°
C) 49°, 49°, 82°
D) 33°, 33°, 114°

Question

Quizplus · Accepted Answer

Let x be the measure of the two congruent angles.
Then the third angle is x + 33.
Since the sum of the angles in a triangle is 180 degrees, we have:
x + x + (x + 33) = 180
Simplifying this equation, we get:
3x + 33 = 180
Subtracting 33 from both sides, we get:
3x = 147
Dividing both sides by 3, we get:
x = 49
Therefore, the two congruent angles are each 49 degrees and the third angle is 33 degrees greater, or 82 degrees.
So the measure of all three angles is 49 degrees, 49 degrees, and 82 degrees. Let x be the measure of each of the two equal angles in the isosceles triangle. Then the third angle is x + 33. The sum of the angles in a triangle is 180 degrees, so we have x + x + (x + 33) = 180. Simplifying the left side of the equation gives us 3x + 33 = 180. Solving for x we get x = 49. Therefore, the three angles are 49°, 49°, and 82°. So, the correct option is C.

Solve the Problem. -In an Isosceles Triangle, One Angle Is 33° Greater Than