MCQ
Two supplementary angles differ by $40^\circ .$ The measure of the larger angle is:
- A$70^\circ$
- B$80^\circ$
- ✓$110^\circ$
- D$100^\circ$
✓
Answer
Correct option: C.
$110^\circ$
Let the larger angle be $x.$
Then, the smaller angle $= (x - 40^\circ )$
As, the sum of the two supplementary angles is always $180^\circ .$
$\Rightarrow x + (x - 40^\circ ) = 180^\circ $
$\Rightarrow 2x - 40^\circ = 180^\circ $
$\Rightarrow 2x = 180^\circ + 40^\circ $
$\Rightarrow 2x = 220^\circ $
$\Rightarrow\text{x}=\frac{220^\circ}{2} ($By transposing $2$ to $R.H.S.)$
$\therefore\text{x}=1106^\circ$
So, the measure of the larger angle is $110^\circ .$
Hence, the correct alternative is option $(c).$
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