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25 votes
25 votes
one angle of a triangle measures 80° more than the smallest, while a third angle is twice the smallest. whats the measure of each angle?

User The Demz
by
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1 Answer

28 votes
28 votes

Answer: The measure of each angle is 105°, 50°, and 25°.

Step-by-step explanation: The first step in solving this is writing down what you know.

In the phrase it tells you that "one angle of a triangle measures 80 more than the smallest", so we can say that one angle = 80 + smallest angle.

This can be simplified more to x = 80 + y

x = One Angle

y = Smallest Angle

Then if we continue with the phrase it says "a third angle is twice the smallest", so we can say that a third angle = 2(Smallest Angle).

This can be simplified more to z = 2(y)

z = Third Angle

We also know that a triangles angles add up to 180°, so we know x + y + z = 180.

So, with these equations we can now solve for x, y, and z.

The easiest way would be to simply just plug in x and z straight into the 180 equation as follows.

x = 80 + y

z = 2(y)

180 = x + y + z

180 = (80 + y) + y + (2y)

180 = 80 + 4y

100 = 4y

y = 25

Then we can use y to solve for the other two equations.

z = 2(25) x = 80 + 25

z = 50 x = 105

After completing that you are left with the three angles of the triangle, 25, 50, and 105.

User Alejandro Barone
by
2.7k points
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