Question

Need help for Geo very Urgent please

Answer 1

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°