Question

For ΔABC, if m∠A + m∠B = 100 and m∠B + m∠C = 130, then find the measures of all the angles of ΔABC.

Answer 1

$\textbf {Hey there, here is the solution.}$

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Sum of angles in a triangle = 180°

.

Given that m∠A + m∠B = 100°

⇒ m∠C = 180 - 100 = 80°

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Given m∠B + m∠C = 130

⇒ m∠B = 130 - 80 = 50°

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Given m∠A + m∠B = 100

⇒ m∠A = 100 - 50 = 50°

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Answer: m∠A = 50° , m∠B = 50° and m∠C = 80°

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$\textbf {Cheers}$

Answer 2

Hi ,

It is given that ,

In ∆ABC ,

m<A + m<B = 100 ------( 1 )

m<B + m<C = 130° ------( 2 )

We know that ,

m<A + m<B + m<C = 180° ---( 3 )

[ Angle sum property ]

substitute ( 1 ) in equation ( 3 ) , we get

100 + m<C = 180

m<C = 180 - 100 = 80

Substitute m<C = 80° in ( 2 ), we get

m<B = 130 - 80 = 50°

Substitute m<B = 50° in ( 1 ) we get

m<A = 100 - 50 = 50°

Therefore ,

In ∆ABC ,

m<A = m<B = 50° ,

m<C = 80°

I hope this helps you.

: )