Question

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

a) 45°
b) 60°
c) 75°
d) 90°

Answer 1

After adding the three given angles of the quadrilateral and subtracting the sum from 360°, we find that the fourth angle should be 165°, not matching any of the provided options.

Step-by-step explanation:

To find the size of the fourth angle in a quadrilateral, recall that the sum of all angles in any quadrilateral is 360°. Therefore, to find the missing angle, you subtract the sum of the known angles from 360°:

• Sum of known angles: 60° + 30° + 105° = 195°
• Sum of all angles in a quadrilateral: 360°
• The fourth angle = 360° - 195° = 165°

However, since the options provided do not include 165°, it's likely that there was a mistake in the given options or in the question itself.