Question

How do u do this????

Answer 1

Let's consider what the question asks for:

--> find the value of 'x'

The function gives us a quadrilateral

--> separated into two triangles

In the triangle that has one angle with measure 65 degrees

-->it is an isosceles triangle thus the top most angle in that triangle is also

65 degrees

--> the other unknown angle is, therefore:

`\text{unknown angle} + 65 + 65 = 180\\\text{unknown angle}+130=180\\\text{unknown angle}=180-130=50\\\text{unknown angle}=50`

Now that unknown angle forms a complementary relationship with the angle of the other triangle.

`50 + \text{bottom most angle of other triangle}=90\\\text{bottom most angle of other triangle}=90-50\\\text{bottom most angle of other triangle}=40`

Now that the bottom triangle

--> has an angle with measure 'x'

--> that triangle is also an isosceles

--> meaning that our triangle's angle looks like this

`40 + x+x+180\\2x+40=180\\2x=140\\x=70`

Answer: 70