Question

If a quadrilateral has three angles that are equal to 60°, 30°, and 105°, what is the size of the fourth angle?

a) 120°
b) 135°
c) 150°
d) 165°

Answer 1

The fourth angle of a quadrilateral with angles of 60°, 30°, and 105° is 165°, which is found by subtracting the sum of the known angles from 360 degrees.

Step-by-step explanation:

To find the size of the fourth angle in a quadrilateral, we must use the knowledge that the sum of the interior angles in any quadrilateral is 360 degrees. Since we already know three of the angles, we can add them together and subtract the sum from 360 degrees to find the measure of the fourth angle.

Let's calculate it step by step:

1. Add the known angles: 60° + 30° + 105° = 195°.
2. Subtract the sum of the known angles from the total degrees in a quadrilateral: 360° - 195° = 165°.

Therefore, the size of the fourth angle is 165°. The correct answer is option d) 165°.