Question

question 1 - 32
if in a triangle ( abc ), ( abcong ac ), and ( mangle b = 50^{circ} ), what is the value of ( mangle a )?
( 50^{circ} )
( 80^{circ} )
( 100^{circ} )
( 130^{circ} )

Explanation:

Step1: Identify triangle type

Since \( AB \cong AC \), triangle \( ABC \) is isosceles with \( \angle B \cong \angle C \).

Step2: Find \( m\angle C \)

Given \( m\angle B = 50^\circ \), so \( m\angle C = 50^\circ \).

Step3: Use triangle angle sum

The sum of angles in a triangle is \( 180^\circ \). Let \( m\angle A = x \). Then \( x + 50^\circ + 50^\circ = 180^\circ \).

Step4: Solve for \( x \)

\( x = 180^\circ - 50^\circ - 50^\circ = 80^\circ \).

Answer:

\( 80^\circ \) (corresponding to the option with \( 80^\circ \))