Mathematics

Find x; if $$\angle\, 1\, =\, 5x\, +\, 15^{\circ}$$ and $$\angle\, 2\, =\, 28x$$, angles form linear pair.


ANSWER

$$5^{\circ}$$


SOLUTION
$$\angle \, 1\, +\, \angle\, 2\, =\, 180^{\circ}$$ (Linear pair)
$$\Rightarrow\quad 5x\, +\, 15^{\circ}\, +\, 28x\, =\, 180^{\circ}$$
$$\Rightarrow\quad 33x\, =\, 180^{\circ}\, -\, 15\, =\, 165^{\circ}$$
$$\Rightarrow\quad x\, =\, \displaystyle \frac {165^{\circ}}{33}\, =\, 5^{\circ}$$.
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