Question

Calculate the value of x in the given figure

Answer 1

let solve this.....

Produce CD to cut AB at E.
Now, in ∆BDE, we have,
Exterior ∠CDB = ∠CEB + ∠DBE
⇒ x = ∠CEB + 45 …..(i)

In ∆AEC, we have,
Exterior ∠CEB = ∠CAB + ∠ACE
= 55 + 30 = 85

Putting ∠CEB = 85 in (i), we get,
x = 85 + 45 = 130

∴ x = 130

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Answer 2

Given:

Angle CDB=x

To find:

The value of x

Solution:

The value of x=130°.

We can find the measure by following the steps given-

In the given figure, we will extend the line CD so that it touches AB at a point E.

Now, in triangle AEC,

Angle EAC=55° and angle ECA=30°

We know that angle AEC+ angle EAC+ angle ECA=180° (Sum of angles in a triangle)

Putting the values, we get'

Angle AEC+55°+30°=180°

Angle AEC+85°=180°

Angle AEC=180°-85°=95°

We know that AB is a straight line.

So, angle AEC+angle DEB=180° (Linear pair)

On putting the values,

95°+angle DEB=180°

Angle DEB=180°-95°=85°

In triangle DEB, the sum of all angles will be equal to 180°.

Angle DEB+angle DBE+angle BDE=180°

85°+45°+angle BDE=180°

130°+angle BDE=180°

Angle BDE=180°-130°=50°

Similarly, CE is a straight line.

Angle BDE+angle BDC=180° (Linear pair)

Angle BDC=x°

50°+x=180°

x=180°-50°

x=130°

Therefore, the value of x=130°.