Question

2.4 assignment
10 of 10
possible points: 1.88
in △abc, ∠a≅∠c and ∠b is a right - angle. find the measure of each angle.
∠a =
∠b =
∠c =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$, i.e., $\angle A+\angle B+\angle C = 180^{\circ}$.

Step2: Substitute the value of $\angle B$

Since $\angle B = 90^{\circ}$, the equation becomes $\angle A+\ 90^{\circ}+\angle C=180^{\circ}$, which simplifies to $\angle A+\angle C=180^{\circ}-90^{\circ}=90^{\circ}$.

Step3: Use the given angle - equality

Given that $\angle A\cong\angle C$, let $\angle A = x$ and $\angle C=x$. Then $x + x=90^{\circ}$, or $2x = 90^{\circ}$.

Step4: Solve for $x$

Dividing both sides of $2x = 90^{\circ}$ by 2, we get $x=\frac{90^{\circ}}{2}=45^{\circ}$.

Answer:

$\angle A = 45^{\circ}$
$\angle B = 90^{\circ}$
$\angle C = 45^{\circ}$