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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the
third angle is 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer: The LARGEST angle has a measure of

Sagot :

Answer:

The LARGEST angle has a measure of 81°

Step-by-step explanation:

Let α be the smallest angle

     β be the second angle

     θ be the third angle.

• One (second) angle in a triangle has a measure that is three times as large as the smallest angle.

Then

β = 3α

• The measure of thethird angle is 45 degrees more than that of the smallest angle.

Then

θ = α + 45

• We know that the sum of the interior angles of a triangle add up to 180°

Then

α + β + θ = 180

Then

α + (3α) + (α + 45) = 180

Then

5α + 45 = 180

Then

5α = 135

Then

α = 27

_______________

β = 3α = 3 × 27 = 81

θ = α + 45 = 45 + 27 = 72

Conclusion :

The LARGEST angle has a measure of 81°

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