A convex quadrilateral has interior angle measures of 2c+34°, 146°, 77°, and 99°. What is the value of c?

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Answer 1 · 2018-02-25T20:41:44

#c = 2^@#

in all quadrilaterals, the sum of the interior angles is #360^@#.

#(2c + 34)^@ + 146^@ + 77^@ + 99^@ = 360^@#

expanding brackets, this gives

#2c + 34^@ + 146^@ + 77^@ + 99^@ = 360^@#

adding all the numbers gives

#2c + 356^@ = 360^@#

subtracting #356^@# gives

#2c = 4^@#

dividing by #2# gives

#c = 2^@#