Question

question 3 points 2 the two triangles are congruent. find the missing angles. image of two triangles, triangle abc with angle b=44°, angle c=53°; triangle def options: angles a = 93°, e = 44°, f = 53°, d = 93°; angles a = 83°, e = 44°, f = 53°, d = 83°; angles a = 44°, e = 83°, f = 53°, d = 44°; angles a = 53°, e = 44°, f = 83°, d = 53°

Explanation:

Step1: Find angle A in triangle ABC

The sum of angles in a triangle is \(180^\circ\). In \(\triangle ABC\), we know \(\angle B = 44^\circ\) and \(\angle C = 53^\circ\). So, \(\angle A=180^\circ - 44^\circ - 53^\circ\).
Calculating: \(180 - 44 - 53 = 83^\circ\), so \(\angle A = 83^\circ\).

Step2: Use congruence of triangles

Since \(\triangle ABC \cong \triangle EFD\) (congruent triangles), corresponding angles are equal. So, \(\angle E=\angle B = 44^\circ\), \(\angle F=\angle C = 53^\circ\), and \(\angle D=\angle A = 83^\circ\).

Answer:

Angles \( A = 83^\circ \), \( E = 44^\circ \), \( F = 53^\circ \), \( D = 83^\circ \) (the second option: Angles \( A = 83^\circ \), \( E = 44^\circ \), \( F = 53^\circ \), \( D = 83^\circ \))