Question

in △abc, line segments ac ≅ bc and m∠bca = 70°. 15. what is the measure of ∠abc? a. 20° b. 35° c. 55° d. 70°

Explanation:

Step1: Identify the triangle type

Since $AC\cong BC$, $\triangle ABC$ is isosceles. In an isosceles triangle, base - angles are equal.

Step2: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle A=\angle ABC = x$. We know that $\angle BCA = 70^{\circ}$. So, $x + x+70^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Combining like - terms, we get $2x=180^{\circ}- 70^{\circ}=110^{\circ}$. Then $x=\frac{110^{\circ}}{2}=55^{\circ}$.

Answer:

C. $55^{\circ}$