$△ A B C$ $triangleABC$ is isosceles, where AB=BC. If $m ∠ A = 5 x + 30$ $m angleA= 5x+ 30$ and $m ∠ B = 2 x$ $mangleB= 2x$ , then how do you find $m ∠ C$ $mangleC$ ?

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$△ A B C$ $triangleABC$ is isosceles, where AB=BC. If $m ∠ A = 5 x + 30$ $m angleA= 5x+ 30$ and $m ∠ B = 2 x$ $mangleB= 2x$ , then how do you find $m ∠ C$ $mangleC$ ?

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Answer 1 · 2016-12-27T18:11:08

Please see the explanation.

Explanation:

Given: $∠ A = 5 x + 30^{\circ}, ∠ B = 2 x, and A B = B C$ $angle A = 5x + 30^@, angle B = 2x, and AB = BC$

I am going to use the notation where the side opposite the angle has the same letter but in lowercase. In this notation, AB becomes side c and BC becomes side a, therefore, AB = BC becomes c = a

Because c = a, we know that $∠ A = ∠ C = 5 x + 30^{\circ}$ $angle A = angle C = 5x + 30^@$ ; this allows us to write the following equation:

$∠ A + ∠ B + ∠ C = 180^{\circ}$ $angle A + angle B + angle C = 180^@$

Substitute the corresponding functions of x:

$5 x + 30 + 2 x + 5 x + 30 = 180^{\circ}$ $5x + 30 + 2x + 5x + 30 = 180^@$

Solve for x:

$12 x + 60^{2} = 180^{\circ}$ $12x + 60^2 = 180^@$

$12 x = 120^{\circ}$ $12x = 120^@$

$x = 10^{\circ}$ $x = 10^@$

$∠ C = 5 (10^{\circ}) + 30^{\circ}$ $angle C = 5(10^@) + 30^@$

$∠ C = 80^{\circ}$ $angle C = 80^@$

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$△ A B C$ $triangleABC$ is isosceles, where AB=BC. If $m ∠ A = 5 x + 30$ $m angleA= 5x+ 30$ and $m ∠ B = 2 x$ $mangleB= 2x$ , then how do you find $m ∠ C$ $mangleC$ ?

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triangleABC△ABCtriangleABC is isosceles, where AB=BC. If m angleA= 5x+ 30m∠A=5x+30m angleA= 5x+ 30 and mangleB= 2xm∠B=2xmangleB= 2x, then how do you find mangleCm∠CmangleC?

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Explanation:

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$△ A B C$ $triangleABC$ is isosceles, where AB=BC. If $m ∠ A = 5 x + 30$ $m angleA= 5x+ 30$ and $m ∠ B = 2 x$ $mangleB= 2x$ , then how do you find $m ∠ C$ $mangleC$ ?