The difference between the measure of an angle x and twice its reflex is 51°. What is the value of x?

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Solution

It is given that, the difference between the measure of an angle x and twice its reflex is 51°.
Reflex of $x = 360 ° - x$
Since $x$ and twice its reflex differs by 51°, we have,
$x - 2 (360 ° - x) = 51 °$
$x - 2 \times 360 ° + 2 x = 51 °$
$x + 2 x = 720 ° + 51 °$
$3 x = 771 °$
$x = \frac{771 °}{3} = 257 °$
Hence, the value of x is equal to 257°.

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