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

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

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Step-by-step video solution

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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

Step-by-step written solution

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1

Understand the problem

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

2

Step-by-step solution

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.

3

Final Answer

No

Practice Quiz

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If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

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