Question
In a cyclic quadrialteral ABCD , if m ∠ A = 3 (m ∠C). Find m ∠ A.
✓
Answer
m ∠ A = 3 (m ∠C)
∠ A + ∠ C = 180 (Opposite angles of a cyclic quadrilateral)
3∠C + ∠ C = 180
4 ∠ C = 180
∠ C = 45
m ∠ A = 3 (m ∠ C)
= 3 × 45
= 135
m ∠ A = 135°
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In a malaria epidemic, the number of cases diagnosed were as follows:
on what days do the mode and upper and lower quartiles occur?
| Date july | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| num | 5 | 12 | 20 | 27 | 46 | 30 | 31 | 18 | 11 | 5 | 0 | 1 |
Find the value(s) of k for which each of the following quadratic equation has equal roots: $(k + 4)x^2+ (k + 1)x + 1 =0$ Also, find the roots for that value (s) of k in each case.
→Prove the following identity:
$
\frac{\tan ^2 \theta}{\tan ^2 \theta-1}+\frac{\operatorname{cosec}{ }^2 \theta}{\sec ^2 \theta-\operatorname{cosec}^2 \theta}=\frac{1}{\sin ^2 \theta-\cos ^2 \theta}
$
→$
\frac{\tan ^2 \theta}{\tan ^2 \theta-1}+\frac{\operatorname{cosec}{ }^2 \theta}{\sec ^2 \theta-\operatorname{cosec}^2 \theta}=\frac{1}{\sin ^2 \theta-\cos ^2 \theta}
$
In the following figure $, AB$ is the diameter of a circle with centre $O$.
If chord $AC =$ chord $AD,$ Prove that:
$(i)$ arc $BC =$ arc $DB$
$(ii)\ AB$ is bisector of $\angle CAD.$
Further, if the length of arc $AC$ is twice the length of arc $BC,$ find : $(a) \angle BAC\ \ (b) \angle ABC$
→If chord $AC =$ chord $AD,$ Prove that:
$(i)$ arc $BC =$ arc $DB$
$(ii)\ AB$ is bisector of $\angle CAD.$
Further, if the length of arc $AC$ is twice the length of arc $BC,$ find : $(a) \angle BAC\ \ (b) \angle ABC$
A boy is 1.54 m tall. Standing at a distance of 3m in front of a 4.54 m high wall he can just manage to see the sun. Find the angle of elevation of the sun.
Find the length of the chord of a circle in the following when:
Radius is $13 \ cm$ and the distance from the centre is $12 \ cm$
→Radius is $13 \ cm$ and the distance from the centre is $12 \ cm$
An aeroplane is $30 \ m$ long and its model is $15 \ cm$ long. If the total outer surface area of the model is $150 cm^2$, find the cost of painting the outer surface of the aeroplane at Rs. $120$ per $m ^2$, if $50 m^2$ is left out for windows.
→Use a ruler and compass only for this question to construct the cyclic quadrilateral ABCD in which AB = 5 cm, BC = 8 cm, ∠ ABC = $67 \frac{1}{2}^{\circ}$, and D is equidistant from B and C.
→Calculate the amount and the compound interest for the following :
Rs. 12500 for 2 years at 8% for the first year and 10% for the second year.
Rs. 12500 for 2 years at 8% for the first year and 10% for the second year.
An aeroplane when flying at a height of 4km from the ground passes vertically above another aeroplane at an instant when the angles of the elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplanes at that instant.