Question

6. Find x in each of the following figures.
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Answer 1

☆ Solution :

First let us find the value of ∠ABC

So,

→ ∠ABD + ∠ABC = 180° (linear pair)

→ 120° + ∠ABC = 180°

→ ∠ABC = 180° - 120°

→ ∠ABC = 60°

Now,

We can observe a ∆ABC

Therefore, finding the value of x by :

∠BAC + ∠ABC + ∠ACB = 180°

(Angle sum property of triangle)

According to Question,

↬ x + 60° + x + 30° = 180°

↬ x + x + 30° + 60° = 180°

↬ 2x + 90° = 180°

↬ 2x = 180° - 90°

↬ 2x = 90°

↬ x = 90/2

↬ x = 45°

Therefore,

• The value of x(∠A) is 45° respectively.

Answer 2

Answer :-

The Exterior Angle Property of a triangle states that the sum of two interior opposite angles equals to the exterior angle.

Given,

1st Interior Opposite Angle = $x$

2nd Interior Opposite Angle = $(x+30)$

Exterior Angle = $120$°

Hence,

$x+(x+30)=120$

$=>x+x+30=120$

$=>2x+30=120$

$=>2x=120-30$

$=>2x=90$

$=>x=90\div2$

$=>x=45$

Verification :-

LHS = $x+(x+30)$

= $45+(45+30)$

= $45+75$

= $120$°

RHS = $120$°

LHS = RHS  hence, verified.

Thus,

The value of $x$ equals to $45$. Also, 1st interior angle equals to $45$° and the 2nd equals to $75$°.

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$@NightRead$