Q9 of 69 Page 9

In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.

Given,

AB = AC and,


BD = BC


∠2 = ∠3 (Since, AB = AC)


∠4 = ∠5 (Since, BD = BC)


= (i)


In


∠2 = ∠4 + ∠5


∠2 = 2∠4 (Since, ∠4 = ∠5)


∠3 = 2∠4 (Since, ∠3 = ∠2)


=


=


Thus, ∠ACD: ∠ADC = 3: 1


More from this chapter

All 69 →
7

State exterior angle theorem.

 8

If the side BC of Δ ABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

 10

The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.

 11

In Fig. 9.40, if AB||CD, EF||BC, ∠BAC = 65° and ∠DHF = 35°, find ∠AGH.