Question

a right triangle has one angle that measures 33°. what is the measure of the other acute angle?

Explanation:

Step1: Recall angle - sum property of right - triangle

In a right - triangle, one angle is $90^{\circ}$, and the sum of all interior angles of a triangle is $180^{\circ}$. Let the given acute angle be $A = 33^{\circ}$, the right - angle be $B=90^{\circ}$, and the unknown acute angle be $C$.

Step2: Use the angle - sum formula

$A + B+C=180^{\circ}$. Substitute $A = 33^{\circ}$ and $B = 90^{\circ}$ into the formula: $33^{\circ}+90^{\circ}+C = 180^{\circ}$.

Step3: Solve for the unknown angle

$C=180^{\circ}-(33^{\circ}+90^{\circ})=180^{\circ}-123^{\circ}=57^{\circ}$.

Answer:

$57^{\circ}$