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.

Question

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&#xB0; and =118&#xB0; , Find the measure of each angle of the triangle.

Philoid · Accepted 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°

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.

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.