Answer

Verified

456.3k+ views

**Hint:**Join point C and A, to get two triangles $\Delta ADC$ and $\Delta BAC$. Now use the property of cyclic quadrilateral to find the measure of angle $\angle CBA$ and use the property that a triangle with one of its arms as diameter of circle always makes a right angle at the circumference.

**Complete step-by-step answer:**

Given that the $\angle ADC = 130^\circ $ and ABCD is a cyclic quadrilateral, i.e. each pair of opposite angles of ABCD have sum equal to $180^\circ $.

Therefore $\angle CBA + \angle ADC = 180^\circ \Rightarrow \angle CBA = 180^\circ - 130^\circ = 50^\circ $

Let’s now join the points C and A to get triangle $\Delta ADC$ and $\Delta BAC$.

Now in $\Delta BAC$, we use the property which states that any triangle having diameter of a circle as its base will always subtend a right angle at the circumference, i.e. $\angle BCA = 90^\circ $

So, we have got $\angle BCA = 90^\circ $ and $\angle CBA = 50^\circ $ in $\Delta BAC$. Now we can easily calculate the third angle by the property that sum of all the interior angles of a triangle is $180^\circ $

$\angle BAC + \angle ACB + \angle CBA = 180^\circ $

Substituting all the known angles in the above relation, you get

$\angle BAC + 90^\circ + 50^\circ = 180^\circ $

$\angle BAC = 180^\circ - 140^\circ = 40^\circ $

**Option A is the correct answer.**

**Note:**Try to understand every detail mentioned in the question. Don’t assume anything until it's given. A cyclic quadrilateral is defined as a quadrilateral inscribed in a circle with all the points on the circumference. Cyclic quadrilateral can also be termed as inscribed quadrilateral. Getting handy with the properties of circles and quadrilaterals will always help you with these kinds of questions.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you graph the function fx 4x class 9 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE