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

In the right triangle shown, what is the value of $a$ ?

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Explanation

Choice B is correct. The triangle shown is a right triangle, where the interior angle shown with a right angle symbol has a measure of $90 degree$ . It's shown that the other two interior angles measure $13 degree$ and $a °$ . The sum of the measures of the interior angles of a triangle is $180 degree$ ; therefore, $90 + 13 + a = 180$ . Combining like terms on the left-hand side of this equation yields $103 + a = 180$ . Subtracting $103$ from both sides of this equation yields $a equals 77$ .

Choice A is incorrect. This is the measure, in degrees, of the other acute interior angle of the right triangle, not the value of $a$ .

Choice C is incorrect. This is the measure, in degrees, of the right angle of the right triangle, not the value of $a$ .

Choice D is incorrect. This is the sum of the measures, in degrees, of the other two interior angles of the right triangle, not the value of $a$ .