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Answers
Step-by-step explanation:
value of x is 55as
angle c a b is equal to 80 degree as it forms linear pair
now let the ratios be
angle abc is equal to y and angle abd is equal to 3y
3y + y is equal to180 as it forms a straight line therefore y is equal to 45 degree then by angle sum property y +x+80=180 so the value of x is 55 degree
Answer:
here is your answer:
Step-by-step explanation:
let ∠DAB = 1y and ∠BAC = 3y (given; ratio 1:3)
consider line DE,
∠DAB + ∠BAC +∠EAC = 180° ( angles on a straight line)
⇒ y + 3y + 108° = 180° (∠EAC = 108° ; given)
⇒ 4y = 180° - 108°
⇒ 4y = 72°
y = 72°/4
∴ y = 18°
⇒ ∠DAB = 18° and ∠BAC = 3×18°
= 54°
consider ΔDAB,
As DB = AB, ΔDAB is isosceles ⇒ ∠DAB = ∠BDA = 18°
∴ ∠BDA + ∠DAB + ∠ABD = 180° (Angle sum property of triangle)
⇒ 18° + 18° + ∠ABD = 180°
⇒∠ABD = 180° - 36°
∴ ∠ABD = 144°
∠ABD + ∠ABC = 180° (linear pair)
⇒ 144° + ∠ABC = 180°
⇒ ∠ABC = 180° - 144°
∴ ∠ABC = 36° ( YOU CAN DO THIS USING EXTERIOR ANGLE
PROPERTY ALSO)
consider Δ ABC,
∠BAC + ∠ACB + ∠ABC = 180° ( angle sum property of triangle)
54° + x + 36° = 180°
⇒ x + 90° = 180°
⇒ x = 180° - 90°
∴ x= 90°
∴ ∠ACB = x = 90°
hope this helps you!!!!
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(spent a lot of time typing this answer)