The measures of two angles of a triangle are given. Find the m...

Question

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.

17° 41' 13" , 96° 12' 10"

Accepted Answer

Hello, today we're going to be determining the measure of the missing angle of the triangle. So we are given two angle measures of the triangle. We are told that the first angle is 21 degrees, 38 ft and 17 inches. And the second angle is 87 degrees with 19 ft and inches. We want to use this information to determine a third angle which we can label as X. Now recall that a triangle has a total of three sites and the angle sum property for a triangle states that if we add up the values of the three angles of the triangle, the three angles will add up to give us 180 degrees. So what we can go ahead and do is we can use the unknown variable X and the two given angles to set up an equation to solve for the value of X, which is the missing angle. So what we can state is that the first angle which is degrees with 38 ft and 17 inches plus the second angle which is 87 degrees with 19 ft and 21 inches plus the third unknown value which is X is equal to 180 degrees. No, to simplify the left hand side, we can go ahead and add the two known angles together. In order to add the two on angles, we're going to first add the degree portion together. So 21 degrees plus 87 degrees will give us 108 degrees. 38 ft plus 19 ft will give us a total of 57 ft and inches plus 21 inches will give us the value of 38 inches. So what we are left with is 108 degrees with 57 ft and 38 inches plus the unknown value X is equal to 180 degrees. Now, in order to solve for X, we'll need to get X by itself on the left hand side of the equation. In order to do that, we're going to subtract 108 degrees with 57 ft and 38 inches from both sides of the equation. Doing so will give us the new equation which is X is equal to 180 degrees minus degrees with 57 ft and 38 inches. Now, at this step, we need to be careful. We cannot just subtract an angle measure in terms of degrees feet and inches from another angle measure that is only in terms of degrees. We can express 180 degrees in the form of degrees feet and inches. And we are allowed to rewrite 180 degrees as 179 degrees with 59 inches, I mean 59 ft and 60 inches. So if we rewrite 180 degrees, the new equation that we are left with is X is equal to 179 degrees with 59 ft and inches minus 108 degrees with 57 ft and 38 inches. Finally, in order to solve for the unknown value X, we're going to start by subtracting 179 degrees with 108 degrees. 179 minus 108 will give us a final value of 71 degrees. Next 59 ft minus 57 ft will give us a final value of 2 ft and inches minus 38 inches will give us a final value of 22 inches. So what this means is that the missing angle for the triangle is 71 degrees with 2 ft and 22 inches. And with that being said, the answer to this problem is going to be b so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
17° 41' 13" , 96° 12' 10"

Key Concepts

Angle Measurement in Degrees, Minutes, and Seconds

Sum of Angles in a Triangle

Conversion and Subtraction of Angles

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