Question

the track has to meet certain specfications the largest angle, angle c is triple the smallest angle, angle B. Angle, A is double the smallest angle, angle B all of the angles add to 180 degrees. create a equation to represent the sum of the angles ( using varaibles) and then solve for the varaibles to find the measure of the angles

Answer 1

Answer:

$\angle A=\mathbf{60^{\circ}}\\\angle B=\mathbf{30^{\circ}}\\\angle C=\mathbf{90^{\circ}}$

Step-by-step explanation:

Given

Angle C is triple that of angle B.

Angle A is double of angle B

Suppose the angle B is $x$

So, angle A and C are $2x$ and $3x$

$\angle A=2x$

$\angle B=x$

$\angle C=3x$

Add the angles A, B, and C to get $180^{\circ}$

$\Rightarrow \angle A+\angle B+\angle C=18^{\circ}\\\Rightarrow 2x+x+3x=180^{\circ}\\\Rightarrow 6x=180^{\circ}\\\Rightarrow x=30^{\circ}$

$\therefore \angle A=\mathbf{60^{\circ}}\\\angle B=\mathbf{30^{\circ}}\\\angle C=\mathbf{90^{\circ}}$

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