Question

In a triangle, one angle is 20 degrees more than twice another. The measure of the third angle is 10 degrees more than the smallest. What is the measure of each angle?

Answer 1

You know that a triangle adds up to 180° and there is three angles to a triangle, therefore, you get this as your opening equation:\[180° = Angle _{A} + Angle_{B} + Angle_{C}\]
The first clue is given to states that one angle is 20 degrees more than twice another. We could use Angle A and Angle B for this:
\[Angle_{A} = 20° + 2(Angle_{B})\]Our next clue is that the third angle is 10 degrees more than the smallest. We can use Angle B and Angle C for this:
\[Angle_{B} = 10° + Angle_{C}\]Now we insert all our clues into our first equation to find out one of the angles. Let's try to aim for Angle C:
\[180° = 20° + 2(Angle_{B}) + 10° + Angle_{C} + Angle_{C}\]becomes\[180° = 20° + 2(10° + Angle_{C}) + 10° + Angle_{C} + Angle_{C}\]distribute it out and collect like terms and then solve for Angle C. From there you can plug Angle C into your other equations to solve for the other two.