Question

An architect designs two similar triangular patios. The first patio has angle measures of (x + 25)°, (y + 10)°, and 40°. The second patio has angle measures of (x – 20)°, 55°, and 85°. Find the values of x and y.

a) x = 45°, y = 30°
b) x = 20°, y = 5°
c) x = 60°, y = 15°
d) x = 70°, y = 40°

Answer 1

To find the values of x and y, we can use the fact that the angles in a triangle sum to 180 degrees. For the first patio, we have (x + 25)° + (y + 10)° + 40° = 180°. Simplifying, we get x + y + 75° = 180°. Similarly, for the second patio, we have (x - 20)° + 55° + 85° = 180°, which simplifies to x + 120° = 180°. Solving these equations, we find that x = 45° and y = 30°. Therefore, the correct answer is option a) x = 45°, y = 30°.

Step-by-step explanation:

To find the values of x and y, we can use the fact that the angles in a triangle sum to 180 degrees.

For the first patio, we have (x + 25)° + (y + 10)° + 40° = 180°.

Simplifying, we get x + y + 75° = 180°.

Similarly, for the second patio, we have (x - 20)° + 55° + 85° = 180°, which simplifies to x + 120° = 180°.

Solving these equations, we find that x = 45° and y = 30°. Therefore, the correct answer is option a) x = 45°, y = 30°.