Direct answers :
In triangle 1 :
[tex]\color{plum}\tt \: \bold{\tt m∠1 = 77.7°}[/tex]
In triangle 2 :
[tex]\color{plum}\bold{\tt \: m∠B =63 °}[/tex]
[tex]\color{plum}\bold{\tt \: m∠C =63° }[/tex]
In triangle 3 :
[tex]\color{plum}\bold{\tt \: m∠1 = 40° }[/tex]
[tex]\color{plum}\bold{\tt \: m∠2 = 28°}[/tex]
Steps to derive the correct measurement of each of the angles :
In triangle 1 :
Given :
Sum of all angles in a triangle = 180°
Which means :
[tex] =\tt 180 - (52.2 + 50.1)[/tex]
[tex] =\tt 180 - 102.3[/tex]
[tex] = \tt77.7°[/tex]
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 :
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 :
[tex] =\tt 54 + 2x = 180[/tex]
[tex] = \tt180 - 54 = 2x[/tex]
[tex] =\tt 2x = 126[/tex]
[tex] =\tt x = \frac{126}{2} [/tex]
[tex] =\tt x = 63[/tex]
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)
[tex] = \tt140 - 112 = ∠2[/tex]
[tex] = \tt \: m∠2 = 28°[/tex]
Thus, the measure of angle 2 = 28°
= m∠1 + m∠2 + m∠3 = 180°
[tex] =\tt m∠1 + 112 + 28 = 180[/tex]
[tex] =\tt m∠1 + 140 = 180[/tex]
[tex] = \tt \: m∠1 = 180 - 140[/tex]
[tex] = \tt \: m∠1 = 40°[/tex]
Thus, the measure of angle 1 = 40°
