Exterior angles are outside the triangle. The measure of the ∠B in ΔABC is 92°
What is the exterior angle?
The exterior angle is the angle formed by extending a line from one side of the triangle. It is always supplementary to the corresponding side angle.
Given to us
∠B = 2x
∠A = x+2
We know that ∠BCD is the exterior angle of the angel ∠C, therefore,
[tex]\angle BCD + \angle C = 180^o\\[/tex]
Substitute the value of the ∠BCD,
[tex]140^o + \angle C = 180^o\\\\\angle C = 180^o -140^o\\\\\angle C = 40^o[/tex]
thus, the measure of the ∠C = 40°
We know that the sum of all the angles of the triangle is equal to 180°, therefore,
∠A + ∠B + ∠C = 180°
[tex](x+2) + 2x + 40^o = 180^o\\\\x+2+2x =180-40\\\\3x + 2 = 140\\\\3x = 140-2\\\\x = 46^o[/tex]
As we know the value of x now, substitute the value of x in the ∠B,
∠B = 2x
∠B = 2(46)
∠B = 92°
hence, the measure of the ∠B in ΔABC is 92°
Learn more about Exterior Angles:
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