Question

Q.4
In AABC, if BC=AB and B=80°, then A equals to​

Answer 1

➤ Correct Question :-

In∆ABC, if BC = AB and ∠B = 80°, then find ∠A.

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★ How to do :-

Here, we are given with a triangle that has two sides equal. The triangle which has two sides as equal is said to be an isosceles triangle. The triangle which has two sides equal will also have two angles equal and the other different. In this question, we are given with the measurement of an angle of isosceles triangle. We are asked to find the other angle in this triangle. To find. the answer, we use the concept of angle sum property of the triangle. Thai concept says that all the angles in a triangle together adds up to 180°. If no, then it's not considered as a triangle. So, let's solve!!

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➤ Solution :-

${\sf \longrightarrow \underline{\boxed{\sf {Angle \: sum \: property}_{(Triangle)} = {180}^{\circ}}}}$

Substitute the given values.

${\tt \leadsto {80}^{\circ} + x + x = {180}^{\circ}}$

Add both variables together.

${\tt \leadsto {80}^{\circ} + 2x = {180}^{\circ}}$

Shift the number 80 from LHS to RHS, changing it's sign.

${\tt \leadsto 2x = 180 - 80}$

Subtract the value on RHS.

${\tt \leadsto 2x = 100}$

Shift the number 2 from LHS to RHS.

${\tt \leadsto x = \dfrac{100}{2}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = {50}^{\circ}}$

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${\red{\underline{\boxed{\bf So, \: the \: \angle{A} \: measures \: {50}^{\circ}}}}}$

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Verification :-

${\tt \leadsto {80}^{\circ} + x + x = {180}^{\circ}}$

Substitute the value of x.

${\tt \leadsto {80}^{\circ} + {50}^{\circ} + {50}^{\circ} = {180}^{\circ}}$

Remove the degree symbol which makes easier to solve.

${\tt \leadsto 80 + 50 + 50 = 180}$

Add the values on LHS.

${\tt \leadsto 180 = 180}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!