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

Question

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.  147° 12' , 30° 19'

Accepted Answer

Hello, today we're going to be determining the measure of the missing angle of the triangle. So we are given two known angles for a given triangle. We are told that the first angle is 131 degrees with ft and the second angle is 25 degrees with ft. We want to use these two angles to help us find a third, unknown angle which we can label as X. Now recall that a triangle has a total of three angles and the angle sum property for a triangle states that the sum of the three angles inside of a triangle will equal to 180 degrees. So if we wanted to solve for our unknown angle measure X, we'll need to take the sum of the three angles that are given to us. So we're going to write the first angle which is degrees with 32 ft plus the second angle which is 25 degrees with 17 ft and will be adding an unknown angle X and set it equal to degrees. Now, what we wanna do is we want to solve for X, we can start by adding the two known angles together. Now, in order to add these two angles, we're going to start by adding the degree components together. 131 degrees plus 25 degrees will give us a sum of 156 degrees. 32 ft plus 17 ft will give us a sum of 49 ft. So what we are left with is 156 degrees with 49 ft plus an unknown angle, X is equal to 180 degrees. Now, in order to sol for X, we're going to have to subtract 156 degrees with ft to both sides of the equation doing so will leave us with X is equal to 180 degrees minus degrees with 49 ft. Now, at this part of the equation, we need to be careful. We cannot take the difference of an angle in terms of degrees with another angle. In terms of degrees and feet. We're going to have to rewrite 180 degrees as an angle measure. In terms of degrees and feet, we can rewrite 180 degrees as degrees with 60 ft. If we replace 180 degrees with this new value, the new equation we are left with is X is equal to 179 degrees with 60 ft minus 156 degrees with 49 ft. Finally, we'll be taking the difference of these two angles. So we're going to start with the difference of the degree components. 179 degrees minus 156 degrees will give us a final difference of 23 degrees and 60 ft minus 49 ft will give us a difference of 11 ft. So that means the unknown angle to the triangle is degrees with 11 ft. 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. 147° 12' , 30° 19'

Key Concepts

Triangle Angle Sum Theorem

Angle Measurement in Degrees and Minutes

Conversion of Angle Units

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