Question : The sum of two angles of a triangle is 116° and their difference is 24°. The measure of the smallest angle of the triangle is:
Option 1: 38°
Option 2: 28°
Option 3: 46°
Option 4: 64°
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Correct Answer: 46°
Solution :
Let the angles be $x$ and $y$.
According to the question,
$x+y=116°$ -----(1)
$x-y=24°$ ------(2)
Solving equation 1 and 2, we get
$x$ = 70°, $y$ = 46°
Third angle = 180° – 70° – 46° = 64°
So, the smallest angle is 46°.
Hence, the correct answer is 46°.
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