Question

What type of triangle is XYZ based on the angle ratio of 3:5:7, and what is the measure of each angle?

a) Scalene triangle; 45°, 75°, 105°
b) Isosceles triangle; 30°, 50°, 70°
c) Equilateral triangle; 60°, 60°, 60°
d) Obtuse-angled triangle; 30°, 50°, 100°

Answer 1

The triangle XYZ is a scalene triangle with angles measured at 36°, 60°, and 84° based on the angle ratio of 3:5:7.

Therefore, the correct answer is a) Scalene triangle; 36°, 60°, 84°.

Step-by-step explanation:

The question asks us to determine the type of triangle XYZ and the measurement of its angles based on the given ratio 3:5:7. Let's solve this step-by-step:

1. First, we know that the sum of the angles in any triangle is 180 degrees.
2. Since the ratio of the angles is 3:5:7, we can represent the angles as 3x, 5x, and 7x, where x is a common multiplier.
3. Adding these angle expressions together (3x + 5x + 7x) gives us 15x, which should equal 180 degrees.
4. Dividing 180 degrees by 15 gives us x = 12 degrees.
5. Multiplying each part of the ratio by this multiplier gives us the angles: 3x = 36°, 5x = 60°, and 7x = 84°.
6. The triangle is scalene, as all sides and angles are different.
7. No angle is greater than or equal to 90°, so it's not an obtuse triangle, and no two angles are the same, so it is not isosceles or equilateral either.

Therefore, the correct answer is a) Scalene triangle; 36°, 60°, 84°.