Question

Find angle SIR in step by step​

Answer 1

Step-by-step explanation:

Solution :-

From the given figure,

In ∆ NLM,

NM || SR

∠NSR = 95°

NSR = 95° ∠RMN = 45°

We have,

∠NSR and ∠LSR are linear pair

Therefore, ∠NSR + ∠ LSR = 180°

=> 95° + ∠ LSR = 180°

=> ∠ LSR = 180°-95°

=> ∠ LSR = 85°

and

NM || SR and RM is a transversal then

∠LRS and ∠ RMN are corresponding angles

We know that

Corresponding angles are equal.

Therefore, ∠ LRS = ∠ RMN

=> ∠ LRS = 45°

In ∆ SLR,

By Interior angles sum property

∠SLR + ∠LRS + ∠ LSR = 180°

=> ∠ SLR + 45° +85° = 180°

=> ∠ SLR + 130° = 180°

=> ∠SLR = 180°-130°

=> ∠ SLR = 50°

Answer :-

The measure of the angle SLR = 50°

Used formulae:-

→ If two parallel lines are intersected by a transversal then the corresponding angles are equal.

→ The sum of the three interior angles in a triangle is 180°.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Solution :-

From the given figure,

In ∆ NLM,

NM || SR

∠NSR = 95°

NSR = 95° ∠RMN = 45°

We have,

∠NSR and ∠LSR are linear pair

Therefore, ∠NSR + ∠ LSR = 180°

=> 95° + ∠ LSR = 180°

=> ∠ LSR = 180°-95°

=> ∠ LSR = 85°

and

NM || SR and RM is a transversal then

∠LRS and ∠ RMN are corresponding angles

We know that

Corresponding angles are equal.

Therefore, ∠ LRS = ∠ RMN

=> ∠ LRS = 45°

In ∆ SLR,

By Interior angles sum property

∠SLR + ∠LRS + ∠ LSR = 180°

=> ∠ SLR + 45° +85° = 180°

=> ∠ SLR + 130° = 180°

=> ∠SLR = 180°-130°

=> ∠ SLR = 50°

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