MCQ
Mark against the correct answer in the following:Two supplementary angles differ by $20^\circ .$ The smaller of the two measures:
- A$60^\circ$
- ✓$80^\circ$
- C$100^\circ$
- D$120^\circ$
✓
Answer
Correct option: B.
$80^\circ$
Let first angle $= x$
Then second $= 180^\circ - x$
$x - (180^\circ - x) = 20^\circ $
$\Rightarrow x - 180^\circ + x = 20^\circ $
$\Rightarrow 2x = 20^\circ + 180^\circ = 200^\circ $
$x = 100^\circ $
Second angle $= 180^\circ - 100^\circ = 80^\circ $
Smaller angle $= 80^\circ $
Then second $= 180^\circ - x$
$x - (180^\circ - x) = 20^\circ $
$\Rightarrow x - 180^\circ + x = 20^\circ $
$\Rightarrow 2x = 20^\circ + 180^\circ = 200^\circ $
$x = 100^\circ $
Second angle $= 180^\circ - 100^\circ = 80^\circ $
Smaller angle $= 80^\circ $
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