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Ex.10.5 Q4 Circles Solution - NCERT Maths Class 9

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In the given figure, \(\begin {align} \angle {ABC}=69^{\circ} \end {align}\) and \(\begin {align} \angle {ACB}=31^{\circ} \end {align}\)find \(\begin {align} \angle {BDC} . \end {align}\)

 Video Solution
Ex 10.5 | Question 4

Text Solution

What is known?

Two angles in a triangle.

What is unknown?

Value of \(\begin {align} \angle {BDC}\end {align}\)


  • Sum of angles in a triangle is \(\begin {align} 180^{\circ}.\end {align}\)
  • Angles in the same segment are equal.


Consider the \(\begin {align} \Delta {ABC,}\end {align}\) the sum of all angles will be \(\begin {align} 180^\circ.\end {align}\)

\[\begin{align} \angle {ABC}+ \!\!\angle {BAC}+ \!\angle {ACB} &=180^{\circ} \\ 69^{\circ}+\angle {BAC}+31^{\circ} &=180^{\circ} \end{align}\]

\[\begin{align}  \angle {BAC} &=180^{\circ}-\left(69^{\circ}+31^{\circ}\right) \\ &=180^{\circ}-100^{\circ} \\ &=80^{\circ} \end{align}\]

We know that, angles in the same segment of a circle are equal.

\[\begin {align} ∴ \angle {BDC}=\angle {BAC}=80^{\circ} \end {align}\]

 Video Solution
Ex 10.5 | Question 4
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