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Geometry and Trigonometry Difficulty: Medium

Triangles $A B C$ and $D E F$ are congruent, where $A$ corresponds to $D$ , and $B$ and $E$ are right angles. The measure of angle $A$ is $69 degree$ . What is the measure, in degrees, of angle $F$ ?

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Explanation

The correct answer is $21$ . It's given that triangles $A B C$ and $D E F$ are congruent with angle $A$ corresponding to angle $D$ . Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It's given that the measure of angle $A$ is $69 degree$ . It follows that the measure of angle $D$ is also $69 degree$ . It's given that angle $E$ is a right angle. Therefore, the measure of angle $E$ is $90 degree$ . Let $x$ represent the measure, in degrees, of angle $F$ . Since the measures of the angles in a triangle sum to $180 degree$ , it follows that $69 + 90 + x = 180$ , or $159 + x = 180$ . Subtracting $159$ from both sides of this equation yields $x equals 21$ . Therefore, the measure, in degrees, of angle $F$ is $21$ .