If the measures of the interior angles at vertex A,B, and C are (5x−60∘),(2x+40∘), and (3x−80∘) , respectively, then find the measure of x in the given triangle.
A
28∘
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B
26∘
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C
32∘
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D
30∘
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Solution
The correct option is A28∘ Given: The measures of the interior angles at vertex A,B, and C are (5x−60∘),(2x+40∘), and (3x−80∘), respectively.
As per the angle sum property, the sum of the three interior angles of a triangle is 180∘.
So,
(5x−60∘)+(2x+40∘)+(3x−80∘)=180∘⇒5x−60∘+2x+40∘+3x−80∘=180∘ (Opening the brackets) (5x+2x+3x)+(−60∘+40∘−80∘)=180∘ (Grouping the like terms together) ⇒10x−100∘=180∘ ⇒10x−100∘+100∘=180∘+100∘ (Adding 100∘ on both sides of the equation) ⇒10x=280∘ ⇒x=28∘