Question

reasoning

1. if ∠tap and ∠bre are supplementary and ∠bre is its own complement, find the measure of ∠tap. show how you arrived at your answer.

Explanation:

Step1: Define self - complementary angle

Let the measure of $\angle BRE=x$. Since $\angle BRE$ is its own complement, we have $x + x=90^{\circ}$ (by the definition of complementary angles where the sum of two complementary angles is $90^{\circ}$).
$2x = 90^{\circ}$

Step2: Solve for the measure of $\angle BRE$

Dividing both sides of the equation $2x = 90^{\circ}$ by 2, we get $x=\frac{90^{\circ}}{2}=45^{\circ}$. So, $m\angle BRE = 45^{\circ}$.

Step3: Use the supplementary - angle relationship

Since $\angle TAP$ and $\angle BRE$ are supplementary, and the sum of two supplementary angles is $180^{\circ}$. Let $m\angle TAP = y$. Then $y+m\angle BRE=180^{\circ}$.
Substituting $m\angle BRE = 45^{\circ}$ into the equation, we have $y + 45^{\circ}=180^{\circ}$.

Step4: Solve for the measure of $\angle TAP$

Subtracting $45^{\circ}$ from both sides of the equation $y + 45^{\circ}=180^{\circ}$, we get $y=180^{\circ}-45^{\circ}=135^{\circ}$.

Answer:

$135^{\circ}$