Question

In triangle ABC, angleA=56°, angleB=4x+10° and angleC=3x-26°
(¡) make an equation in , and solve for x
(¡¡) Calculate the measure of each angle of the triangle
(iv) calculate the measure of the exterior angle at C
(v) verify that the measure of an exterior angle is sum of the two opposite interior angles

Answer 1

Answer:

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Answer 2

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Step-by-step explanation:

In triangle sum of all angles =180

Angle A+angleB+angleC=180°

=>56°+4x+10+3x-26=180°

=>40+7x=180°

=>7x. =180°-40°

=>7x=140°

Therefore x=140°/7

= 20°

Angle A=56°

Angle B=4x+10

=4*20+10

=90°

Angle C=3x-26

= 3*20-26

=34°

iv) angle c +exterior =180°{since it make a straight angle =180}

Angle C=>34+exterior angle=180

Exterior angle =180-34

= 146°

V) :- to prove sum of opposite angles of a Δ=exterior angle

Let angle A=56°{from upper case}

And angle B=90°

So the exterior angle at angle C=sum of opposite anles

Exterior angle=56°+90°

=146°

Hence proved from upper case that exterior angle =146°