Question

in the given figure if angle ADC equals to 118 degree then the measure of angle bdc is​

Answer 1

Answer:

Given angle ADC= 118°

Angle ADB= 90° (angle in a semicircle is half of 180°)

Angle ADC= Angle ADB+ Angle BDC

118° = 90+ Angle BDC

Angle BDC = 118-90

Angle BDC = 28°

hope this will help you

Answer 2

Given:

∠ADC = 118°

To Find:

The measures of ∠BDC

Solution:

It is given that ∠ADC = 118°

Angles in the semi-circle is half of 180°

So, ∠ADB = 90° [half of 180°]

And now, to find the measure of ∠BDC,

∠ADC = ∠ADB + ∠BDC

⇒ 118° = 90° + ∠BDC [∠ADC=118°(given) and ∠ADB=90°]

⇒ ∠BDC = 118° - 90°

⇒ ∠BDC = 28°

Or, the other way to solve this is,

Angle in a segment are equal so,

∠ADB = ∠BCD

∠BCD = 90° [Angle of semi circle]

Now, ∠ADB=118°(given) and ∠BCD=90°

∠ADB + ∠BDC = 118°

substituting the measures of the angles.

⇒ 90° + ∠BDC = 118°

⇒ ∠BDC = 118° - 90°

⇒ ∠BDC = 28°

Therefore, the measure of ∠BDC = 28°.