Answer:
C. 55°
Explanation:
You want the measure of angle A = x+61 in the triangle where the other two angles are marked (x+51) and 80°.
Angle Sum
The sum of angles in a triangle is 180°, so we have ...
(x +61)° +(x +51°) +80° = 180°
2x = -12 . . . . . . . . . . . . . . divide by ° and subtract 192
x = -6 . . . . . . . . . . divide by 2
Angle A
Using this value of x in the expression for angle A, we find that angle to be ...
∠A = x +61 = -6 +61 = 55 . . . . degrees
The measure of angle A is 55 degrees.
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Additional comment
In the attached, we have formulated an expression for x that should have a value of 0: 2x+12 = 0. The solution is readily found to be x=-6, as above. We used that value to find the measures of all of the angles in the triangle. The other angle is 45°.
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