Question

in a parallelogram the opposite angles have the same measures. each of the two larger angles in a parallelogram is 15° less than 4 times the smaller angles. find the measure of each angle. the two smaller angles are each □°.

Explanation:

Step1: Set up the equation

Let the measure of the smaller angle be $x$. Then the measure of the larger angle is $4x - 15$. In a parallelogram, adjacent - angles are supplementary, so $x+(4x - 15)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x + 4x-15=5x - 15$. So the equation becomes $5x-15 = 180$.

Step3: Add 15 to both sides of the equation

$5x-15 + 15=180 + 15$, which simplifies to $5x=195$.

Step4: Solve for x

Divide both sides of the equation by 5: $\frac{5x}{5}=\frac{195}{5}$, so $x = 39$.

Answer:

39