Unknown Interior Angles

Geometry Level 1

The three interior angles in a triangle (in degrees) are $x$ , $y$ , and $x+y$ . What is the measure of the largest angle in the triangle (in degrees)?

The answer is 90.

1 solution

Arron Kau Staff
May 13, 2014

Since $x$ and $y$ are angles they must be positive. Thus we have $x < x+y$ and $y < x+y$ . Hence $x+y$ is the largest angle.

The interior angles of the triangle must sum to $180^\circ$ . So we have $x + y + (x + y) = 180^\circ$ $\Rightarrow x + y = 90^\circ$ . Hence the largest angle in the triangle is $90^\circ$ .

Unknown Interior Angles

The answer is 90.

1 solution

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