Question

In a triangle ABC, if AB=AC and BC is produced to D such that ∠ACD=100° , then calculate ∠A.

Answer 1

$\huge{ \tt{♕︎ sᴏℓᴜᴛɪᴏɴ ♕︎}}$

➨We have ,

→ ZACD + ZACB = 180 ° [ Linear Pair ]

→ 100 ° + ZACB = 180 °

→ ZACB = 180 ° - 100 °

→ ZACB = 80 °

➨From ( i ) & ( ii ) ,

➨ We get

➨ Angle ZABC = Angle ZACB = 80 °

➨Now ,

→ ZABC + ZACB + ZA = 180º .... [ Sum of the 3 interior angles of a triangle is 180° ]

→ Substituting the values of ZABC & ZACB ,

➨ We get

→ 80 ° + 80 ° + A = 180 °

→ 160 ° + ZA = 180 °

→ ZA = 180 ° - 160 °

→ ZA = 20 °

Thus , the measure of Angle ‘A’ is 20 °

Answer 2

Answer:

20°

Step-by-step explanation:

In ∆ABC, AB = AC

∴ ∠B = ∠C

But Ext. ∠ACD = ∠A + ∠B

∠ACB + ∠ACD = 180° (Linear pair)

∴ ∠ACB + 100° = 180°

⇒ ∠ACB = 180°-100° = 80°

∴ ∠B = ∠ACD = 80°

But ∠A + ∠B 4- ∠C = 180°

∴ ∠A + 80° + 80° = 180°

⇒∠A+ 160°= 180°

∴ ∠A= 180°- 160° = 20°