Question

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Just find x

Answer 1

Answer:

x = 50°

Step-by-step explanation:

Let's make 2 equations based on the properties of the triangles :

Applying Exterior Angle Property :

1. x + 2∠1 = 2√2 (taking ΔABC in perspective)
2. ∠1 + 25 = √2 (taking ΔBDC in perspective)

Divide equation 1 by 2 :

⇒ 1/2 (x + 2∠1) = 1/2 x (2∠2)

⇒ x/2 + ∠1 = ∠2

⇒ ∠2 - ∠1 = x/2

Similarly, rewrite equation 2 :

⇒ ∠1 + 25 = ∠2

⇒ ∠2 - ∠1 = 25

From these 2 equations, we get :

⇒ x/2 = 25

⇒ x = 25 × 2

⇒ x = 50°

Answer 2

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's consider the figure with two triangles,

Angle b is divided into two equal parts :

• let's name each of them as y ~

and similarly

Exterior angle C is divided into two equal parts :

• let's name each of them z ~

Now, according to exterior Angle property :

In Triangle ABC

$\qquad \sf  \dashrightarrow \:2y + x = 2z \: \: \: \:$

$\qquad \sf  \dashrightarrow \: 2z - 2y = x \: \: \: \:$

$\qquad \sf  \dashrightarrow \:2(z - y) = x$

$\qquad \sf  \dashrightarrow \:z - y = \dfrac{x}{2} \: \: \: \: \: \: \: - (1)$

and in Triangle BDC

$\qquad \sf  \dashrightarrow \:y + 25 = z \: \: \: \: \: \: \:$

$\qquad \sf  \dashrightarrow \:z - y = 25 \: \: \: \: \: \: \: - (2)$

equate equation (1) and (2) :

$\qquad \sf  \dashrightarrow \: \dfrac{x}{2} = 25$

$\qquad \sf  \dashrightarrow \: {x}{} = 25 \times 2$

$\qquad \sf  \dashrightarrow \: {x}{} = 50 \degree$