Question

the measure of one angle of a quadrilateral is 10° greater than the smallest angle, the third angle is 11° greater than twice the smallest angle, and the fourth angle is 24° greater than the smallest angle. find the measure of the smallest angle.

Explanation:

Step1: Let the smallest angle be $x$.

Let the smallest angle be $x$. Then the second - angle is $x + 10$, the third - angle is $2x+11$, and the fourth - angle is $x + 24$.

Step2: Use the angle - sum property of a quadrilateral.

The sum of the interior angles of a quadrilateral is $360^{\circ}$. So, $x+(x + 10)+(2x+11)+(x + 24)=360$.

Step3: Combine like terms.

Combining like terms gives $(x+x+2x+x)+(10 + 11+24)=360$, which simplifies to $5x+45 = 360$.

Step4: Solve for $x$.

Subtract 45 from both sides: $5x=360 - 45=315$. Then divide both sides by 5: $x=\frac{315}{5}=63$.

Answer:

$63$