Question:
Tick (✓) the correct answer:
If one angle of a parallelogram is 24° less than twice the smallest angle then the largest angle of the parallelogram is
(a) 68°
(b) 102°
(c) 112°
(d) 176°
Solution:
(c) $112^{\circ}$
Let $x^{\circ}$ be the smallest angle of the parallelogram.
$T$ he sum of adjacent angles of a parallelogram is $180^{\circ}$.
$\therefore x+2 x-24=180$
$\Rightarrow 3 x-24=180$
$\Rightarrow 3 x=180+24$
$\Rightarrow 3 x=204$
$\Rightarrow x=\frac{204}{3}$
$\Rightarrow x=68$
$\therefore$ Smallest angle $=68^{\circ}$
$L$ argest angle $=(180-68)^{\circ}=112^{\circ}$
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