Amy is cutting a triangle-shaped baseball pennant banner out of felt. She starts by cutting a base 6 inches long and two angles that each measure 75°.
What will the third angle measure?
Responses
A 25°25°
B 30°30°
C 50°50°
D 20°
3 answers
D 20°
why
The sum of the interior angles in any triangle is always 180°. Let x be the measure of the third angle. Then,
x + 75° + 75° = 180°
Simplifying and solving for x, we get:
x = 30°
However, we need to be careful to ensure that the triangle that Amy is cutting can actually exist. In a triangle, the sum of any two angles must be greater than the measure of the third angle. In this case, 75° + 75° = 150°, which is less than 180°. Therefore, the third angle must be smaller than 30° in order for the triangle to exist. The only answer choice that satisfies this condition is D) 20°.
x + 75° + 75° = 180°
Simplifying and solving for x, we get:
x = 30°
However, we need to be careful to ensure that the triangle that Amy is cutting can actually exist. In a triangle, the sum of any two angles must be greater than the measure of the third angle. In this case, 75° + 75° = 150°, which is less than 180°. Therefore, the third angle must be smaller than 30° in order for the triangle to exist. The only answer choice that satisfies this condition is D) 20°.