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°

Rate this question :

Each question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

In the given figure, PQ>PR and QS and RS are the bisectors of ∠Q and ∠R respectively. Show that SQ>SR

RS Aggarwal & V Aggarwal - Mathematics

In, if -=42°and-=21°, Find,and.

RS Aggarwal & V Aggarwal - MathematicsOf the three angles of a triangle, one is twice the smallest and mother one is thrice the smallest. Find the angle.

RS Aggarwal & V Aggarwal - MathematicsOf the three angles of a triangle are equal and the third angle is greater than each one of them by 18°. Find the angle.

RS Aggarwal & V Aggarwal - MathematicsTwo adjacent angles on a straight line are in the ratio 5:4 Find the measure of each one of these angles.

RS Aggarwal & V Aggarwal - MathematicsIn the adjoining figure, AC>AB and AD is the bisector of ∠A. show that ∠ADC>∠ADB.

RS Aggarwal & V Aggarwal - Mathematics

In the given figure, ABC is a triangle in which::=3:2:1 and AC CD. Find the measure of.

RS Aggarwal & V Aggarwal - Mathematics

In ∆ABC, ∠B=35°,∠C=65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

RS Aggarwal & V Aggarwal - Mathematics

In ∆ABC, side AB is produced to D such that BD=BC. If ∠B=60° and ∠A=70°, prove that (i) AD>CD and (ii) AD>AC.

RS Aggarwal & V Aggarwal - Mathematics