Question

① each of borks bags contains the same number of marbles. he has twice as many bags as he has marbles in each bag. if he has 32 marbles in all, how many are in each bag? ② how many angles (less than 180°) are in the figure below?

Explanation:

Step1: Let the number of marbles in each bag be $x$.

The number of bags is $2x$. The total number of marbles is the product of the number of marbles in each bag and the number of bags, so $x\times2x = 32$, which simplifies to $2x^{2}=32$.

Step2: Solve the equation for $x$.

Divide both sides of $2x^{2}=32$ by 2: $x^{2}=16$. Then take the square - root of both sides. Since $x$ represents the number of marbles in a bag (a non - negative quantity), $x = 4$.

Step3: For the angle - counting problem.

The formula to find the number of angles less than $180^{\circ}$ formed by $n$ rays with a common endpoint is $\frac{n(n - 1)}{2}$. Here, $n=9$ (count the number of rays). So the number of angles is $\frac{9\times(9 - 1)}{2}=\frac{9\times8}{2}=36$.

Answer:

1. 4
2. 36