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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

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 $18 degree$ . What is the measure of angle $F$ ?

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Explanation

Choice B is correct. It’s given that triangle $A B C$ is congruent to triangle $D E F$ . Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It’s given that angle $A$ corresponds to angle $D$ , and that the measure of angle $A$ is $18 degree$ . It's also given that the measures of angles $B$ and $E$ are $90 degree$ . Since these angles have equal measure, they are corresponding angles. It follows that angle $C$ corresponds to angle $F$ . Let $x °$ represent the measure of angle $C$ . Since the sum of the measures of the interior angles of a triangle is $180 degree$ , it follows that $18 ° + 90 ° + x ° = 180 °$ , or $108 ° + x ° = 180 °$ . Subtracting $108 degree$ from both sides of this equation yields $x degree equals 72 degree$ . Therefore, the measure of angle $C$ is $72 degree$ . Since angle $C$ corresponds to angle $F$ , it follows that the measure of angle $F$ is also $72 degree$ .

Choice A is incorrect. This is the measure of angle $D$ , not the measure of angle $F$ .

Choice C is incorrect. This is the measure of angle $E$ , not the measure of angle $F$ .

Choice D is incorrect. This is the sum of the measures of angles $E$ and $F$ , not the measure of angle $F$ .