Question Video: Finding the Measure of an Angle given Its Supplementary Angle’s Measure

In the given figure, Matthew stated that 𝑥 is an obtuse angle measuring 105°, and Daniel stated that 𝑥 is an acute angle measuring 75°. Determine which of the two is correct without using a protractor.

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Video Transcript

In the given figure, Matthew stated that 𝑥 is an obtuse angle measuring 105 degrees, and Daniel stated that 𝑥 is an acute angle measuring 75 degrees. Determine which of the two is correct without using a protractor.

In the diagram, we’re given three angles: a 63-degree angle, a 42-degree angle, and 𝑥. We’re told here not to use a protractor, so we shouldn’t try and measure angle 𝑥 directly. When we see this type of instruction, especially in an exam question, very often the actual angle isn’t drawn accurately.

We’ll therefore need to find a way to work out the value of 𝑥 without measuring. That way, we’ll be able to tell whether Matthew is correct or Daniel is correct. You may have already noticed that these three angles sit upon a straight line. And we should remember that the angles on a straight line add up to 180 degrees. We can also say that these three angles are supplementary as supplementary angles add up to 180 degrees.

If we add the value of the two other angles, 63 degrees and 42 degrees, well, 60 and 40 would give us 100, and three and two would give us five. So we know that these two angles would add to 105 degrees. But we need to find the value of the angle 𝑥, which is remaining. Since these three angles add to 180 degrees, we would calculate 180 degrees subtract 105 degrees, which gives us the value of 75 degrees. As Daniel was the person who correctly identified that 𝑥 is 75 degrees, then Daniel would be our answer.

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