Chapter 7.3, Problem 10ST1

To determine

To calculate: $\angle R,\angle S,\angle T$

Answer to Problem 10ST1

  $\angle R=45°,\angle S=75°,\angle T=60°$

Explanation of Solution

Given information: $\Delta ABC\sim \Delta RST,\angle A=45°,\angle C=60°$

Formula used: According to angle sum property of a triangle, sum of all angles of a triangle is equal to $180°$ .

Calculation:

According to angle sum property of a triangle, sum of all angles of a triangle is equal to $180°$ .

First find $\angle B$

In $\Delta ABC$ ,

  $\angle A+\angle B+\angle C=180°$

Put $\angle A=45°,\angle C=60°$

  $\begin{array}{l}45°+\angle B+60°=180°\\ \Rightarrow \angle B+105°=180°\\ \Rightarrow \angle B=180°-105°=75°\end{array}$

So,

  $\angle A=45°,\angle B=75°,\angle C=60°$

Two triangles are said to be similar if the following conditions are satisfied:

1. Corresponding sides of the triangles are proportional.
2. Corresponding angles of the triangles s are equal.

As $\Delta ABC\sim \Delta RST,$

  $\angle R=\angle A=45°,\angle S=\angle B=75°,\angle T=\angle C=60°$

So,

  $\angle R=45°,\angle S=75°,\angle T=60°$