Question

find the value of x​

Answer 1

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Answer 2

Answer:

110°

Step-by-step explanation:

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Concept:

• Angle Sum Property of a ∆: Angles of a ∆ add up to 180°.
• Linear Pair Axiom- adjacent angles on a straight line add up to 180°
• Isosceles triangle property- Base angles of isosceles∆ are equal
• Exterior angle property= Exterior angle is equal to the sum of Interior opposite angles of a ∆

Solution:

Given, in ∆ABC(let) , as AB = AC [ given]

==> ∆ ABC is isosceles.

==>angle ABC = angle ACB

Now, as angle BAC = 40°, using Angle Sum Property of ∆,

Angle BAC + angle ABC + angle ACB = 180°

==> 40° + 2angle ABC = 180°

==> 2angle ABC = 180° - 40°

==> 2angle ABC = 140°

==> angle ABC = 70°

Now, using exterior angle property of ∆ [ also can use linear pair axiom],

Let the side BC be produced to D.

==> angle ACD = angle ABC + angle BAC

==> x = 70° + 40°

==> x = 110°

Thus the answer is 110°

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