Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. a coat hanger is in the shape of isosceles triangle abc shown in the figure. sides ab and bc are congruent. if m∠bac = 22°, then m∠abc = °. reset next

Explanation:

Step1: Identify triangle type

Since \( AB \cong BC \), \( \triangle ABC \) is isosceles with \( \angle BAC \cong \angle BCA \). Given \( m\angle BAC = 22^\circ \), so \( m\angle BCA = 22^\circ \).

Step2: Sum of angles in triangle

The sum of angles in a triangle is \( 180^\circ \). Let \( m\angle ABC = x \). Then \( 22^\circ + 22^\circ + x = 180^\circ \).

Step3: Solve for \( x \)

Simplify: \( 44^\circ + x = 180^\circ \). Subtract \( 44^\circ \) from both sides: \( x = 180^\circ - 44^\circ = 136^\circ \).

Answer:

\( 136 \)