Question

Q5. In triangle ABC side BC is extended to D. Angle ABC=30°, Angle ACD=160°, find Angle BAC​

Answer 1

Answer:

Angle BAC = 130°

Step-by-step explanation:

In given triangle ABC

Angle ABC = 30°

Angle ACD = 160°

as we know

Angle ACB + Angle ACD = 180° ( sum of the angles on a straight line is 180°)

Angle ACB + 160° = 180°

Angle ACB = 20°

now sum of the angles in a triangle is 180°

Angle ABC + Angle ACB + Angle BAC = 180°

30° + 20° + Angle BAC = 180°

Angle BAC = 130°

Answer 2

Question

In triangle ABC side BC is extended to D. ∠ABC=30°, ∠ACD=160°, find ∠BAC.

Answer

Value of ∠BAC is 130°

Given

• ∠ABC = 30°
• ∠ACD = 160°

To Find

• Value of ∠BAC

Calculations

We know that Exterior Angle equals to Sum of two Interior Opposite Angles.

So, In △ABC

• Exterior Angle = ∠ACD

• Opposite Interior Angles = ∠ABC and ∠BAC

Exterior Angle = Sum of 2 Interior Opp. Angles

➞ ∠ACD = ∠ABC + ∠BAC

➞ 160° = 30° + ∠BAC

➞ 160° - 30° = ∠BAC

➞ 130° = ∠BAC

➞ ∠BAC = 130°

Hence, value of ∠BAC = 130°.