Question

MNOP is a rhombus. If angle OMP=(3x+2) degrees and angle NOP=(4x+40) degrees find angle MPO and angle NMO

Answer 1

Since MNOP is a rhombus, all four angles of the rhombus are equal. Let's call this common angle measure "a".

So, angle MPO = angle NMO = angle OMP = angle NOP = a.

Given that angle OMP = (3x + 2) degrees and angle NOP = (4x + 40) degrees, we can set up the following equation:

a = (3x + 2) = (4x + 40)

Simplifying the equation, we get:

3x + 2 = 4x + 40
2 - 40 = 4x - 3x
-38 = x

Now, substituting the value of x back into one of the equations, we can solve for "a":

a = (3(-38) + 2)
a = -114 + 2
a = -112

So, angle MPO = angle NMO = angle OMP = angle NOP = a = -112 degrees.