Question

triangle abc is similar to triangle rst.
what is the measure of angle acb of the smaller triangle? (note: the triangles are not drawn to scale.)
a 124° b 108° c 115° d 119°

Explanation:

Step1: Identify corresponding angles

Since $\triangle ABC \sim \triangle RST$, $\angle A = \angle R$, $\angle B = \angle S$, $\angle C = \angle T$.

Step2: Find $\angle R$ via triangle sum

Sum of angles in a triangle is $180^\circ$. For $\triangle RST$:
$\angle R = 180^\circ - 36^\circ - \angle T$
First confirm $\angle A = \angle R$: $\angle A = 25^\circ$, so $\angle R = 25^\circ$.

Step3: Calculate $\angle ACB$ (=$\angle T$)

$\angle ACB = 180^\circ - \angle A - \angle B$
$\angle B = \angle S = 36^\circ$, so:
$\angle ACB = 180^\circ - 25^\circ - 36^\circ$

Answer:

D. $119^\circ$