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Need help for Geo very Urgent please

Need help for Geo very Urgent please-example-1

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Direct answers :

In triangle 1 :


\color{plum}\tt \: \bold{\tt m∠1 = 77.7°}

In triangle 2 :


\color{plum}\bold{\tt \: m∠B =63 °}


\color{plum}\bold{\tt \: m∠C =63° }

In triangle 3 :


\color{plum}\bold{\tt \: m∠1 = 40° }


\color{plum}\bold{\tt \: m∠2 = 28°}

Steps to derive the correct measurement of each of the angles :

In triangle 1 :

Given :

  • m∠2 = 52.2°
  • m∠3 = 50.1°

Sum of all angles in a triangle = 180°

Which means :


=\tt 180 - (52.2 + 50.1)


=\tt 180 - 102.3


= \tt77.7°

Thus, the measure of angle 1 = 77.7°

Since the sum of all angles (77.7+52.2+50.1=180°) equals 180° we can conclude that we have found out the correct value of angle 1.

Therefore, the m∠1 = 77.7°

In triangle 2 :

Given :

  • m∠A = 54°
  • m∠B = m∠C

Let the measure of angle B be x.

Then, the measure of angle C will also be x.

Which means the sum of angle B and C will be equal to 2x.

That means :


=\tt 54 + 2x = 180


= \tt180 - 54 = 2x


=\tt 2x = 126


=\tt x = (126)/(2)


=\tt x = 63

Thus, the measure of Angle B = 63°

Measure of angle C = 63°

In triangle 3 :

Given :

  • m∠3 = 112°
  • Measure of exterior angle = 140°

Which means :

= m∠2 + 112° = 140° (exterior angle property)


= \tt140 - 112 = ∠2


= \tt \: m∠2 = 28°

Thus, the measure of angle 2 = 28°

= m∠1 + m∠2 + m∠3 = 180°


=\tt m∠1 + 112 + 28 = 180


=\tt m∠1 + 140 = 180


= \tt \: m∠1 = 180 - 140


= \tt \: m∠1 = 40°

Thus, the measure of angle 1 = 40°

User DragonBobZ
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