Adjacent Angles Analysis: Can Right and Obtuse Angles Share a Side?

Question

Is it possible to have two adjacent angles, one of which is obtuse and the other right?

00:00 Can adjacent angles be one obtuse and one right angle?

00:04 Adjacent angles sum to 180° (straight angle)

00:07 Let's assume one angle is obtuse (greater than 90°)

00:12 And the second is right (equals 90°)

00:18 We can see that the only angle that complements to 180° is a right angle

00:26 Therefore one angle cannot be obtuse and the other right

00:31 And this is the solution to the question

Remember the definition of adjacent angles:

Adjacent angles always complement each other up to one hundred eighty degrees, that is, their sum is 180 degrees.

This situation is impossible since a right angle equals 90 degrees, an obtuse angle is greater than 90 degrees.

Therefore, together their sum will be greater than 180 degrees.