Question

sides of BC, CA and BA of triangle ABC are produced to x, y and z respectively, as shown in figure. angle XCA=120° and angle YAZ=60°. find angles of triangle ABC. what type of triangle is this​

Answer 1

Answer:

bc = to mc a,x 160 120°

Step-by-step explanation:

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Answer 2

Answer:

∠ABC = 60°, ∠ACB = 60°, ∠CAB = 60°

ΔABC is an equilateral triangle

Step-by-step explanation:

In ΔABC,

∠ACB + ∠ACX = 180°

∠ACB + 120° = 180°

∠ACB = 60°... (1)

∠ZAY = ∠CAB = 60°

∠CAB = 60°... (2)

∠ABC + ∠BCA + ∠CAB = 180°   [Angle Sum Property of a  Δ]

∠ABC + 60° + 60° = 180°   [Substituting from (1) and (2)]

∠ABC = 60°... (3)

∠ABC = 60°

∠ACB = 60°

∠CAB = 60°

Since all angles are equal, ΔABC is an equilateral triangle.