Q. 164.0( 9 Votes )

In the given figure, the side BC of has been produced on both sides-on the left to D and on the right to E. If =106° and =118°, Find the measure of each angle of the triangle.


Answer :

74°, 62°, 44°


Given, =106° and =118°


ABD + ABC = 180° [Because DC is a straight line]


106° + ABC = 180°


ABC = 74°_______________ (i)


ACB + ACE = 180° [Because BE is a straight line]


ACB + 118° = 180°


ACB = 62°_______________ (ii)


Now, triangle ABC


ABC + ACB + BAC = 180° [Sum of angles of triangle]


74° + 62° + BAC = 180° [From equation (i) and (ii)]


BAC = 44°


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