Question

In a isosceles triangle one angle is 57° greater than each of the other two equal angles. find a measure of all three angles

Answer 1

An Isosceles triangle has two sides and two angles to be congruent or equal.

Let the two congruent angles be x° degrees, then the third side which is 57° greater than the congruent angles would measure (x+57°).

SKETCH

The sum of angles in a triangle is 180°. Hence,

`\begin{gathered} x+x+(x+57)=180^0 \\ 3x+57=180^0 \\ 3x=180-57 \\ 3x=123 \\ x=(123)/(3) \\ x=41^0 \\ \therefore(x+57)=41^0+57^0=98^0 \end{gathered}`

Therefore, the measure of all three angles are: 41,⁰ 41⁰, and 98⁰