Respuesta :
A triangle is a three-edged polygon with three vertices. The measurement of the largest angle of the triangle is 93°.
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Let the measure of the smallest angle be x. And as it is given that the measure of the second angle is 3 times the smallest, while the measure of the third angle is 25 more than the smallest angle. Therefore, the measure of the angles can be written as,
∠1 = x
∠2 = 3x
∠3 = x + 25
Since the sum of all the angles of a triangle is 180°, therefore, the sum can be written as,
∠1 + ∠2 + ∠3 = 180°
x + 3x + (x+25) = 180°
x + 3x + x + 25 = 180°
5x + 25 = 180°
5x = 180° - 25°
5x = 155°
x = 31°
Now, the measurement of all the angles is,
∠1 = x = 31°
∠2 = 3x = 3(31°) = 93°
∠3 = x + 25 = (31+25)° = 56°
Hence, the measurement of the largest angle of the triangle is 93°.
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