Question

in triangle abc , ab=ac and bc is produced d such that acd = 100* find angle a?

Answer 1

Given :

• In ΔABC :
• AB = AC
• BC Produced to D
• ∠ACD = 100°

To find :

• ∠A

Solution :

• In ΔABC :
• AB = AC
• ∠ACD = 100°
• ∠ACB + ∠ACD = 180°   (Linear Pair)
• 3∠ACB + 100° = 180°
• ∠ACB = 80°
• ∠ACB = ∠ABC = 80°

☯ Measure of ∠ACB and ∠ABC = 80°

• In ΔABC :
• ∠ABC + ∠ACB + ∠BAC = 180°
• 80° + 80° + ∠BAC = 180°
• 160° + ∠BAC = 180°
• ∠BAC = 180° - 160°
• ∠BAC = 20°

☯ Measure of ∠BAC = 20°

☯ Hence, ∠A = 20°

Answer 2

Answer:

In ΔABC :

AB = AC

∠ACD = 100°

∠ACB + ∠ACD = 180°   (Linear Pair)

3∠ACB + 100° = 180°

∠ACB = 80°

∠ACB = ∠ABC = 80°

☯ Measure of ∠ACB and ∠ABC = 80°

In ΔABC :

∠ABC + ∠ACB + ∠BAC = 180°

80° + 80° + ∠BAC = 180°

160° + ∠BAC = 180°

∠BAC = 180° - 160°

∠BAC = 20°

☯ Measure of ∠BAC = 20°

☯ Hence, ∠A = 20°

Step-by-step explanation: