Given a triangle with one angle measuring 65 degrees and two equal sides, applying angle sum property and vertically opposite angles helps find angles in both triangles. Resulting in x = 80 degrees.
Observing the figure imagine there are 2 triangles , so in the first triangle we are given the measure of one angle which measures 65 degrees and we are also given that the 2 sides are equal in the figure.
So , as those 2 sides are equal we can say that the opposite angles are also equal making another angle measure 65 degrees.
Now , we can use the angle sum property to find out the measure of the remaining angle.
65 + 65 + y = 180 ( assuming that one angle is y )
130 + y = 180
y = 50
Now , clearly we can see that y forms a vertically opposite angles with the second triangle so the measure of that angle would be 50 degrees.
And we also can see that 2 sides are given equal so the 2 opposite angles will be equal
So , by this we have found the measure of 2 angles of the second triangle and we are now supposed to find the value of x .
By using angle sum property of a triangle we can find that value.
50 + 50 + x = 180
x = 80 .
So , the measure of x is going to be 80 degrees.