Math, asked by shwetahiremath654, 4 months ago

Q1.Answer the following questions





1) How many parts a circle can divide a plane into?

2) Which is the longest chord of the circle?

3) In the given figure, O is the center of the circle with chords AP and BP being produced to

R and Q respectively. If ∠QPR = 35°, find the measure of ∠AOB.

4) Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each

of the equal angles of the quadrilateral

5) In the given figure, what is the measure of angle x?

6) A side of equilateral triangle is 6cm. Find its area​

Answers

Answered by muskan10453
0

Answer:

(1)A circle divides the plane into three parts:

(2)chord that passes through the center of a circle is called a diameter and is the longest chord.

(3)

∠APB = ∠RPQ = 35°

Now, ∠AOB and ∠APB are angles subtended by an arc AB at centre and at the remaining part of the circle .

∴∠AOB = 2∠APB = 2 × 35° = 70°

(4)Let each equal angle of given quadrilateral be x.

We know that, sum of all interior angles of a quadrilateral is 360°.

∴ x + x + x + 144° = 360°

3x = 360° - 144°

3x = 216°

x = 72°

Hence each equal angle of the quadrilateral is of 72° measures.

(5)

EFD+∠FED=x (Exterior angle property of a triangle)

⇒28

o

+42

o

=∠x

⇒∠x=70

(6)

Step-by-step explanation:

a=6cm, b=6cm, c=6cm

∴s=

2

a+b+c

=

2

6+6+6

=9cm

∴ Area of the equilateral triangle

=

s(s−a)(s−b)(s−c)

=

9(9−6)(9−6)(9−6)

=

9(3)(3)(3)

=9

3

cm

2

Answered by itzUNKNOWNking
1

1) How many parts a circle can divide a plane into?

ans.three parts

A circle divides the plane into three parts: The points INSIDE the circle.

2) Which is the longest chord of the circle?

ans.diameter

A chord that passes through the center of a circle is called a diameter and is the longest chord.

3) In the given figure, O is the center of the circle with chords AP and BP being produced to

ans. ∠APBand∠QPR will be equal as they are vertically opposite angles. Also, we know angle made by a chord at point on the circle is half of the angle made at the center of the circle.

4) Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each

ans.Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each of the equal angles of the quadrilateral .

5) In the given figure, what is the measure of angle x?

ans. ∠EFD+∠FED=x (Exterior angle property of a triangle)

⇒28

o

+42

o

=∠x

⇒∠x=70

o

6) A side of equilateral triangle is 6cm. Find its area

ans.a=6cm, b=6cm, c=6cm

∴s=

2

a+b+c

=

2

6+6+6

=9cm

∴ Area of the equilateral triangle

=

s(s−a)(s−b)(s−c)

=

9(9−6)(9−6)(9−6)

=

9(3)(3)(3)

=9

3

cm

2

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