Question

Find the measure of the "?" or "X". Explain or show your

Answer 1

First, I am taking the interior angle E as 'y' to be able to use the angle sum property to find 'x'.

So we can find 'y' by using 'linear pair'.

So Exterior angle 'E'+y=180 Degree.

= 111+y=180

By transposing: y=180-11

And y= 69 degrees.

And now have angles y & 'Angle G' we can use Angle sum property to find 'x'

ACCORDING TO ANFLE SUM PROPERTY OF TRIANGLE: "THE SUM OF ALL THE ANGLES OF A TRIANGLE IS 180 DEGREE"

THEREFOR, y+x+angle G=180 degrees.

= 69 degrees+66 degrees+x=180 degrees

= 135 degrees+x=180 degrees

by transposing,

x= 180 degrees-135 degrees

And, x= 45 degrees

ANOTHER METHOD:

BY USING EXTERIOR ANGLE PROPERTY.

ACCORDING TO EXTERIOR ANGLE PROPERTY OF TRIANGLE: "An exterior angle of a triangle is equal to the sum of its interior opposite angles"

So, Exterior Angle E= x+ Angle G

= 111 degrees= x+ 66 degrees

By transposing, x= 111 degrees-66 degrees

= x=45 degrees.

So no matter whichever method is used, the value of x= 45 degrees.

Answer 2

66⁰ + x = 111⁰

x = 111⁰ - 66⁰

x = 45⁰