How Much Do The Angles Of A Triangle Add Up To

An isosceles triangle has 2 equal sides and two equal angles.

A right triangle has one xc^o angle.

If a triangle is neither isosceles nor correct, we will telephone call it a generic triangle.

The largest angle of a triangle is five times as big every bit the smallest angle. The tertiary angle is 12 degrees more than than the smallest angle. Notice the measure of all three angles.

What are nosotros asked to find in this problem? Look at the last sentence of the trouble, and you will meet that we want to find the measures of all three angles of the triangle.

To define the variables in this problem, we volition first by drawing a picture of a generic triangle:

Since the problem tells united states of america a lot about the largest angle and the middle bending simply not much about the smallest angle, nosotros�ll call the smallest angle 10 degrees.

The largest bending is 5 times the smallest angle, so the largest bending is 5x degrees.

The middle angle is 12 degrees more than the smallest angle, and then we�ll telephone call the heart angle x +12 degrees. We�ll write all of this information in our picture show:

Our equation will come from the fact that the sum of the three angles of any triangle must be 180 degrees. This gives united states of america:

(5x) + (ten + 12) + (10) = 180

Now we�ll solve the equation:

5x + 10 + 12 + x = 180

7x + 12 = 180

7x = 168

x = 24

Then the smallest bending measures 24 degrees.

Have nosotros finished the problem? Non quite. We still need to find the measures of the other 2 angles. We�ll refer back to our triangle to encounter that the largest angle measures 5x=5(24)=120^o, and the center angle measures 10+12=24+12=36^o.

So the three angles measure 24^o, 36^o, and 120^o.

Before we exit the problem, permit�southward check our reply with the words of the problem:

words	check
The largest angle of a triangle is 5 times as big equally the smallest angle.	Is 120 5 times every bit big as 24? Yeah!
The 3rd angle is 12 degrees more than than the smallest bending.	Is 36 equal to 12 more than 24? Yes!
This is a triangle: do the angles all add upwardly to 180 degrees?	24 + 36 + 120 = 180