Question

May I please get help with this. I tried many times to solve them but still couldn’t get the right answers

Answer 1

`\begin{gathered} m\angle P=15^(\circ) \\ m\angle Q=120^(\circ) \\ m\angle R=45^(\circ) \end{gathered}`

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are congruent and their corresponding sides are in equal proportion.

Given that triangles ABC and QPR are similar, then all corresponding angles in both triangles will be congruent.

So we'll have that;

`\begin{gathered} m\angle B=m\angle P=15^(\circ) \\ m\angle C=m\angle R=45^(\circ) \end{gathered}`

Let's go ahead and determine the value of A as seen below;

`\begin{gathered} m\angle A+m\angle B+m\angle C=180\ldots\ldots\ldots(\text{ sum of angles in a triangle)} \\ m\angle A+15+45=180 \\ m\angle A+60=180 \\ m\angle A=180-60 \\ m\angle A=120^(\circ) \end{gathered}`

Since angle A is 120 degrees, then angle Q is also 120 degrees since corresponding angles are equal.