What is the value of r in this circuit

See that messy ugly fraction on the right side of the equation ?  Let's make it easier to write.  

If we multiply the top and bottom of the fraction by the same thing, we won't change the value of the fraction.  Let's multiply top and bottom by R .

The fraction 1 / (1/R + 1/2R)

Multiply top and bottom by R :

The fraction = R / (1 + 1/2) .  

But that's just  R/1.5 .

So 20 = R/1.5

Multiply each side of this equation by 1.5 , and you have . . .

30 = R

This is not even a problem about electrical circuits or resistors.  This is a problem about handling complicated fractions to make them less messy.

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step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°