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BRAINLIEST IF YOU ANSWER FAST AND CORRECT!!! ALSO 100 POINTS!

In the following figure, triangle ABC is a right triangle, and m∠A = 38°. Find the value of n°. Note: the figure is not drawn to scale.
138Β°
128Β°
142Β°
52Β°

BRAINLIEST IF YOU ANSWER FAST AND CORRECT ALSO 100 POINTS In the following figure triangle ABC is a right triangle and mA 38 Find the value of n Note the figure class=

Respuesta :

Solution:

We know that:

  • [tex]\angle A = 38\Β°[/tex]
  • [tex]\angle B = 90\Β°[/tex]
  • [tex]\angle A + \angle B + \angle C = 180[/tex]
  • [tex]\angle C + n = 180[/tex]

Step by step calculations:

1. Substitute the angles in the equation "∠A + ∠B + ∠C = 180" to find ∠C:

  • [tex]\angle A + \angle B + \angle C = 180[/tex]
  • => [tex]38 + 90 + \angle C = 180[/tex]
  • => [tex]128 + \angle C = 180[/tex]
  • => [tex]\angle C = 180 - 128[/tex]
  • => [tex]\bold{\angle C = 52}[/tex]

2. Substitute ∠C in the equation "∠C + n = 180" to find n:

  • [tex]\angle C + n = 180[/tex]
  • => [tex]52 + n = 180[/tex]
  • => [tex]n = 180 - 52[/tex]
  • => [tex]\bold{n = 128}[/tex]

Sum of two interiors=exterior

[tex]\\ \rm\Rrightarrow m<A+m<B=n[/tex]

[tex]\\ \rm\Rrightarrow 38+90=n[/tex]

[tex]\\ \rm\Rrightarrow n=128Β°[/tex]

Option B

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