Question

In the diagram. If AB = AD = BD = DC, then find xº
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given:

AB = AD = BD = DC

To find:

The value of x°

Solution:

The value of x° is 30°.

We can find the angle by following the given steps-

We know that in the given triangle ABD, AB=AD=BD.

Since all the sides are equal, triangle ABD is an equilateral triangle.

So, all the angles of the triangle ABD=60°.

Angle ABD=Angle ADB=Angle DAB=60°.

Now, we know that the angle ADB and the angle BDC form a linear pair as AC is a straight line.

So, angle ADB+angle BDC=180°

On putting the value,

60°+angle BDC=180°

Angle BDC=180°-60°

=120°

Now, in triangle BDC,

BD=DC (given)

So, angle DBC=angle DCB (angles opposite to equal sides are also equal)

The sum of all the angles in triangle BDC=180°

Angle DBC+Angle DCB+AngleBDC=180°

Putting the values,

2×Angle DCB+120°=180°

2×Angle DCB=180°-120°

2×Angle DCB=60°

Angle DCB=x°=30°

Therefore, the value of x° is 30°.