Question

In a ∆ABC, if AB=AC and BC is produced to D such that angle ACD = 100° . then, angle a = a) 20° b)40° c)60° d)80°.
Please give complete mathematical explanation with figure . I will definitely mark the best answer as brainlist . its urgent​

Answer 1

Answer:Given:

In Δ ABC,

AB = AC

BC is produced to D such that ∠ACD = 100°

To find:

The measure of ∠A

Solution:

It is given that,

AB = AC

∴ ∠ABC = ∠ACB ....... [Angles opposite to equal sides are also equal in length] ...... (i)

We have,

∠ACD + ∠ACB = 180° ..... [Linear Pair]

⇒ 100° + ∠ACB = 180°

⇒ ∠ACB = 180° - 100°

⇒ ∠ACB = 80° ..... (ii)

From (i) & (ii), we get

∠ABC = ∠ACB = 80°

Now,

∠ABC + ∠ACB + ∠A = 180° ..... [Sum of the 3 interior angles of a triangle is 180°]

substituting the values of ∠ABC & ∠ACB, we get

⇒ 80° + 80° + ∠A = 180°

⇒ 160° + ∠A = 180°

⇒ ∠A = 180° - 160°

⇒ ∠A = 20°

Thus, the measure of ∠A is 20°

Step-by-step explanation:

Answer 2

Answer:

your answer is

(a) 20°

Step-by-step explanation:

hope this helps you....