Question

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

Answer 1

Sum of two Interiors=Exterior

$\\ \rm\rightarrowtail x+90=148$

$\\ \rm\rightarrowtail x=148-90$

$\\ \rm\rightarrowtail x=58$

Answer 2

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°.