Question

In ΔABC, if AB = AC and ∠ is an exterior angle. If ∠ = 70° , then find al the

Angles of ΔABC​

Answer 1

➤ Correct Question :-

In ΔABC, if AB = AC and ∠ is an exterior angle. If ∠ = 110° , then find all the angles of ΔABC.

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★ How to do :-

Here, we are given with the measurement of an exterior angle of a triangle. We are said that it's an isosceles triangle which has two equal sides AB and AC. We know that an isosceles triangle having two equal sides always has two angles equal. So, we can find the other angle by using the exterior angle. The concepts used here are linear pair of angles and angle sum property. We can use these concepts to solve. So, let's solve!!

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➤ Solution :-

Value of ∠ACB :-

${\: \: \: \: \: \underline{\boxed{\sf Straight \: line \: angle = {180}^{\circ}}}}$

Substitute the given values.

${\tt \leadsto x + {110}^{\circ} ={180}^{\circ}}$

Shift the number 110 from LHS to RHS, changing it's sign.

${\tt \leadsto x = 180 - 110}$

Subtract the values to get the value of x.

${\tt \leadsto x = {70}^{\circ}}$

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We know that the angles ACB and ABC are equal as it's an isosceles triangle.

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Value of ∠BCA :-

${\: \: \: \: \: \underline{\boxed{\sf Angle \: sum \: property = {180}^{\circ}}}}$

Add the angles with their names.

${\tt \leadsto \angle{A} + \angle{B} + \angle{C} = {180}^{\circ}}$

Substitute the given values.

${\tt \leadsto y + 70 + 70 = 180}$

Add both values on LHS.

${\tt \leadsto y + 140 = 180}$

Shift the number 140 from LHS to RHS, changing it's sign.

${\tt \leadsto y = 180 - 140}$

Subtract the values to get the value of y.

${\tt \leadsto y = {40}^{\circ}}$

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Answers :-

$\small\boxed{\begin{array}{cc} \bigstar \: \sf{\angle{BAC} = {40}^{\circ}} \\ \\\bigstar \: \sf{\angle{ABC} = {70}^{\circ}} \\ \\ \bigstar \: \sf{\angle{ACB} = {70}^{\circ}}\end{array}}$