Answer:
[tex]\angle A= 21^\circ\\\angle B =125^\circ\\\angle c = 34^\circ[/tex]
Step-by-step explanation:
We are given the following in the question:
A triangle ABC
Let x be the measure of angle C, then according to the question:
[tex]\angle A = x - 13\\\angle B = 4x - 11\\\angle c = x[/tex]
Now, according to angle sum property of triangle, the sum of all the three angles of triangle is equal to 180 degrees.
Thus, we can write:
[tex]\angle A + \angle B +\angle C = 180^\circ\\[/tex]
Putting values, we get,
[tex]x - 13 + 4x - 11 + x = 180\\6x - 24 = 180\\6x = 204\\x = 34[/tex]
[tex]\angle A = x - 13 = 34-13 = 21^\circ\\\angle B = 4x - 11 = 4(34)-11 = 125^\circ\\\angle c = x = 34^\circ[/tex]
The measure of each angle of the given triangle ABC is;
∠A = 21°
∠B = 125°
∠C = 34°
Let ∠C be x
We are given;
∠A = x - 13
∠B = 4x - 11
Now, we know that the sum of angles in a triangle is 180°. Thus;
∠A + ∠B + ∠C = 180°
Plugging in the relevant values gives;
(x - 13) + (4x - 11) + x = 180°
x - 13 + 4x - 11 + x = 180°
6x - 24 = 180°
6x = 180 + 24
6x = 204
x = 204/6
x = 34°
Thus; ∠C = 34°
Thus;
∠A = 34 - 13
∠A = 21°
∠B = 4(34) - 11
∠B = 136 - 11
∠B = 125°
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