Question

given that triangle abc is similar to triangle def. find the angle b.
options:
$79^\circ$
$180^\circ$
$60^\circ$
$42^\circ$

Explanation:

Step1: Calculate angle B in △ABC

The sum of angles in a triangle is $180^\circ$. So:
$\angle B = 180^\circ - \angle A - \angle C$
$\angle B = 180^\circ - 60^\circ - 79^\circ$

Step2: Verify with similar triangles

△ABC ~ △DEF, so corresponding angles are equal. First find $\angle F$:
$\angle F = 180^\circ - 60^\circ - 42^\circ = 78^\circ$
Match corresponding angles: $\angle A = \angle D = 60^\circ$, $\angle C = \angle F = 79^\circ$ (corrected sum check), so $\angle B = \angle E = 42^\circ$.

Answer:

$42^\circ$