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50 POINTS!!! A side of the triangle below has been extended to form an exterior angle of 148°. Find the value of x.

50 POINTS A Side Of The Triangle Below Has Been Extended To Form An Exterior Angle Of 148 Find The Value Of X class=

Sagot :

Sum of two Interiors=Exterior

[tex]\\ \rm\rightarrowtail x+90=148[/tex]

[tex]\\ \rm\rightarrowtail x=148-90[/tex]

[tex]\\ \rm\rightarrowtail x=58[/tex]

Solution:

First, let's find the interior top angle of the triangle.

1. Finding the top angle of the triangle.

Let the top angle be "y".

We know that:

  • 148 + y = Straight line
  • Straight line = 180

This means that:

  • 180 = 148 + y

Simplify the equation by subtracting 148 both sides to isolate "y".

  • 180 - 148 = 148 - 148 + y
  • 180 - 148 = y
  • 32° = y

Hence, the top angle of the triangle is 32°.

2. Finding the measure of "x":

We know that:

  • Sum of interior angles of triangle = 180°

This means that:

  • 32 + x + (Right angle) = 180

Substitute "Right angle" as 90.

  • 32 + x + 90 = 180                                                      
  • x + 122 = 180

Subtract 122 both sides to isolate x.

  • x + 122 - 122 = 180 - 122
  • x = 58°

Thus, the measure of x is 58°.

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