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Given the measure of angle \(a\) is \(33^\circ\), find the sum of the measures of the complementary angle, supplementary angle, and vertical angle for angle \(a\).

Answer :

The sum of the measures of the complementary, supplementary, and vertical angles for angle a of 33° is 237°.

The question asks for the sum of the measures of the complementary angle, supplementary angle, and vertical angle for angle a, given that angle a is 33°.

The complementary angle to angle a would be one that adds up to 90° with angle a. Since angle a is 33°, the complementary angle would be 90° - 33° = 57°.

The supplementary angle to angle a is one that adds up to 180° with angle a. The supplementary angle would thus be 180° - 33° = 147°.

The vertical angle to angle a shares the same measure as angle a, because vertical angles are equal. So, the vertical angle measure is 33°.

To find the total sum of these angles, you would add 57° + 147° + 33° = 237°.

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Rewritten by : Barada

< a = 33

vertical angles are equal....so the vertical angle also equals 33 degrees

complementary angles add up to 90 degrees
so its complimentary angle is (90 - 33) = 57 degrees

supplementary angles add up to 180 degrees
so its supplementary angle is (180 - 33) = 147 degrees