Question

In Fig. 9.27 <ABC=55°=<ACB. Also <DBC=70°=<DCB. Name the sides which are equal. Find <A and <D​

Answer 1

Given:

∠ABC=55°

∠ACB=55°

∠DBC=70°

∠DCB=70°

To find:

(i) ∠BAC

(ii) ∠BDC

(iii) The name of the sides which are equal.

Solution:

We can simply solve this numerical problem by using the following steps.

Now, as we know, sum of all three angles of a triangle adds up to 180°,

Hence, in ΔBAC,

Sum of all angles in ΔBAC= 180°

Therefore, ∠ABC + ∠ACB + ∠BAC = 180°

⇒ 55° + 55° + ∠BAC = 180° (putting the values of the above mentioned angles)

⇒ 110° + ∠BAC = 180°

⇒∠BAC = 180° - 110° = 70°

Hence, AC = BA, as they are the opposite sides of equal angle.

Now, in Δ BDC

⇒ ∠DBC + ∠DCB + ∠BDC = 180°

⇒ 70° + 70° + ∠BDC = 180° (putting the values of the above-mentioned angels)

⇒ ∠BDC = 180° - 140° = 40°

Hence, CD = BD, as they are the opposite sides of equal angle.

Thus ,as per the question, the final result is that: ∠A will be 70° and ∠D will be 40° and the side AC is equal to BA in ΔBAC and similarly, CD is equal to BD in ΔBDC.