Question

*△ABC ~△PQR , ∠A = 40° and ∠B=35° then find ∠R = ?*
1️⃣ 75°
2️⃣ 15°
3️⃣ 95°
4️⃣ 105°​

Answer 1

Step-by-step explanation:

In ∆ ABC

A+B+C=180

=> C=180-(40+35)=180-75=105

In a relation

∆ABC~∆PQR

=> R=C=105°

Answer 2

Given,

The triangle ABC is similar to the triangle PQR.

$\[\begin{array}{l}\angle A = 40^\circ \\\angle B = 35^\circ \end{array}\]$

To find,

The value of $\[\angle R.\]$

Solution,

Know that the sum of the angles of a triangle is $\[180^\circ .\]$

Therefore,

$\[\begin{array}{l} \Rightarrow \angle C = 180^\circ - \left( {\angle A + \angle B} \right)\\ \Rightarrow \angle C = 180^\circ - \left( {40^\circ + 35^\circ } \right)\\ \Rightarrow \angle C = 180^\circ - 75^\circ \\ \Rightarrow \angle C = 105^\circ \end{array}\]$

Know that in similar triangles the corresponding angles are equal.

Therefore,

$\[ \Rightarrow \angle C = \angle R = 105^\circ \]$

Hence, the correct option is (4) i.e. $\[105^\circ .\]$