Question

The opposite angles of cyclic quadrilateral are(3X+10) and (2X+20). Find the angles.​

Answer 1

Explanation:

Need to FinD :

• We have to find the angles.

We know that,

• The opposite angles of the cyclic quadrilateral are (3x + 10)° and (2x + 20)°. And we have to find the angles.

In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle. The opposite angles in a cyclic quadrilateral add up to 180°. So simply, we just simplify the measures and find the value of x. And at last, we'll find the angles of the quadrilateral.

`\rule{200}{3}`

`\sf \dashrightarrow {(3x\ +\ 10)\ +\ (2x\ +\ 20)\ =\ 180} \\ \\ \\ \sf \dashrightarrow {3x\ +\ 10\ +\ 2x\ +\ 20\ =\ 180} \\ \\ \\ \sf \dashrightarrow {5x\ +\ 30\ =\ 180} \\ \\ \\ \sf \dashrightarrow {5x\ =\ 180\ -\ 30} \\ \\ \\ \sf \dashrightarrow {5x\ =\ 150} \\ \\ \\ \sf \dashrightarrow {x\ =\ \frac{\cancel{150}}{\cancel{5}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 30.}}}}_{\sf \blue{\tiny{Value\ of\ x}}}}`

∴ Hence, the required value of x is 30. Now, let us find out the angles.

`\rule{200}{3}`

First AnglE :

• 3x + 10
• 3(30) + 10
• 90 + 10
• 100

∴ Hence, the measure of the first angle of the quadrilateral is 100°.

`\rule{200}{3}`

Second AnglE :

• 2x + 20
• 2(30) + 20
• 60 + 20
• 80

∴ Hence, the measure of the second angle of the quadrilateral is 80°.

Answer 2

40°

Explanation:

Opposite angles in a cyclic quadrilateral are equal

3x + 10 = 2x + 20

Take away 2x from both sides

x + 10 = 20

Take away 10 from both sides

x = 10

Now that we know the value of x, substitute it back into the equations

3x + 10 = 3 x 10 + 10 = 30 + 10 = 40

2x + 20 = 2 x 10 + 20 = 20 + 20 = 40

Both angles are equal to 40°