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 39°. the two larger angles are each □°

Explanation:

Step1: Let the measure of the smaller angle be $x$.

The measure of the larger angle is $4x - 15$.

Step2: Recall the property of parallelogram angles.

In a parallelogram, adjacent angles are supplementary, so $x+(4x - 15)=180$.

Step3: Simplify the equation.

Combine like - terms: $x + 4x-15=180$, which gives $5x-15 = 180$.

Step4: Solve for $x$.

Add 15 to both sides: $5x=180 + 15=195$. Then divide both sides by 5: $x=\frac{195}{5}=39$.

Step5: Find the measure of the larger angle.

Substitute $x = 39$ into the expression for the larger angle: $4x-15=4\times39-15=156 - 15=141$.

Answer:

The two smaller angles are each $39^{\circ}$, and the two larger angles are each $141^{\circ}$.