Question

In a ΔABC, if AB = AC and BC is produced to D such that ∠ACD = 100°, then find ∠A .​

Answer 1

Answer:

20° answer

AB=AC (given)

=ACD =100°(given)

=B= C (base angle them)

= ACB +ACD=180° linear

=ACB+100°=180°pair axion

=ACB=180°-100°=ACB=80°

We know that , B-C

= B= C= 80°=

A+B+C=180°(angle sum property of )

=80°+80°+A=80° triangle

=A= 20°answer

Answer 2

$\huge{ \tt{♕︎ sᴏℓᴜᴛɪᴏɴ ♕︎}}$

➨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 °