Answer :
Answer:
76 degrees
Step-by-step explanation:
Let the angles be x, y and z
As per given:
- x= 66
- z = 57 + 1/2y
- x+y+z = 180
Considering the first 2 equations in the third one:
- 66 + y + 57 + 1/2y = 180
- 1.5y = 180 - (66+57)
- 1.5y = 57
- y = 57/1.5
- y = 38
So the third angle is:
- z = 57 + 38/2 = 76 degrees
The measure of the second angle in the triangle is 40 degrees and the measure of the third angle is 74 degrees.
The problem is about finding the measure of angles in a triangle. Given that the measure of first angle is 66 degrees, and that the sum of the measures of the angles in a triangle is 180 degrees, let us denote the second angle as x. Hence, the third angle will be 1/2×x + 57 according to the problem.
Therefore, we form an equation representing the sum of the angles of the triangle, which is 66+x+(1/2×x+57)=180. Solving this equation allows us to find the value of x or the measure of the second angle.
This results in x = 40 degrees, which means the second angle measures 40 degrees, and the third angle, which is half of this plus 57, is equal to 74 degrees.
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