# Finding unknown angle

• August 4th 2010, 05:26 PM
haftakhan
Finding unknown angle
Attachment 18442

i want to know how to solve this question to find the x in it.And with explanation as i don't know how to solve it.
• August 4th 2010, 05:57 PM
eumyang
Is that a parallelogram with its lower left corner "cut off"? If so, then imagine that you have this corner. It would form a triangle, with two of angles being are supplemental angles of 3x and 132°. The 3rd would have be 2x.

The sum of these angles is 180°, so the equation is
$(180^{\circ} - 3x) + 48° + 2x = 180^{\circ}$.

Solve for x.
• August 4th 2010, 08:12 PM
haftakhan
where has 48 come from ?
• August 4th 2010, 08:53 PM
eumyang
Quote:

Originally Posted by haftakhan
where has 48 come from ?

It's the supplementary angle for the 132°, one of the three angles in the "torn corner" of the parallelogram.
• August 7th 2010, 03:11 AM
haftakhan
Can u explain it in detail as i cant understand it
• August 7th 2010, 06:16 AM
eumyang
Look at the attached diagram:
Attachment 18467

I've added a "corner" to the parallelogram in your original drawing, and then I enlarged the corner. I'm assuming that this "corner" forms a triangle. The sum of angles a, b, and 2x has to equal 180°.

Angle a is the supplement of 3x, so $a = 180^{\circ} - 3x$. Angle b is the supplement of 132°, so $b = 180^{\circ} - 132^{\circ} = 48^{\circ}$. Therefore, the sum of the angles in this triangle is
$(180^{\circ} - 3x) + 48° + 2x = 180^{\circ}$.