Question

Calculate the value of x in the given figure​

Answer 1

<ADC = <x

= Opposite sides are always equal.

= <x = 50°

pls mark brainliest

Answer 2

$\large \sf { hi \: \: friend : )}$

$\large \sf \star { \: solution : }$

Given :

• ∠BAC = 30°
• ∠ABC = 40°
• ∠CDE = 50°

To Find :

• value of x

Solving :

In Triangle ABC

• By Angle Sum Property

$\\ \large \tt \mapsto \: 30 \degree + 40 \degree + \angle acb = 180 \degree \\ \\ \large \tt \mapsto \: 70 \degree + \angle acb = 180 \degree \\ \\ \large \tt \mapsto \: \angle acb = 180 \degree - 70 \degree\\ \\ \large \sf \therefore \: \angle acb = 110 \degree$

Now,

• Finding ∠ECD

➢ ∠ACB + ∠ECD = 180°

• (linear pair)

Angles along a straight line = 180°

$\\ \large \tt \implies \: \angle ECD = 18 0 \degree - 110 \degree \\ \\ \large \sf \: \therefore \: \angle ECD = 70 \degree$

In Triangle ECD :

• Angle Sum Property

➢ ∠ECD + ∠EDC + ∠CED = 180°

• Take CED = y

$\\ \large \tt \implies \: 70 \degree + 50 \degree + y = 180 \degree \\ \\ \large \tt \implies \: 120 \degree + y = 180 \degree \\ \\ \large \tt \implies \: y = 180 \degree - 120 \degree \\ \\ \large \sf \therefore \: y = 60 \degree$

Now,

• y + x = 180°

(linear pair)

$\\ \large \tt \implies \: x + 60 \degree = 180 \degree \\ \\ \large \tt \implies \: x = 180 \degree - 60 \degree \\ \\ \large \underline{ \boxed{ \sf \therefore \: x = 120 \degree}}$

Alternate Method :

• Angle ECD = 70°

➢ Exterior Angle = Sum of 2 opposite interior angles

⇒ 30° + 40° = ECD

• ECD = 70°

➢ x = Sum of 2 opposite interior angles

⇒ x = 70° + 50°

✓ x = 120°