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Blizzard [7]
3 years ago
11

ABCD is a parallelogram. If mZCDA = 63, then mZABC = _?_ The diagram is not to scale.

Mathematics
1 answer:
nevsk [136]3 years ago
4 0

Answer:

b. 63

Step-by-step explanation:

A Parallelogram is known to be a flat shape quadrilateral which has four opposite sides Each two opposite sides are parallel and are equal in length. The opposite angles are equal.

The above answer is correct because opposite angles of a parallelogram are equal:

m∠CDA = m∠ABC

where m∠CDA = 63

∴ m∠ABC = 63 (answer)

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5/6 and 7/8

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✨ B R A I N L I E S T
miv72 [106K]

1

:x

2

+y

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−6x−9y+13=0

(x−3)

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+(y−

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9

)

2

−9−

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+13=0

(x−3)

2

+(y−

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2

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65

Here,

r

1

=

2

65

C

1

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9

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Equation of another circle-

S

2

:x

2

+y

2

−2x−16y=0

(x−1)

2

+(y−8)

2

−1−64=0

(x−1)

2

+(y−8)

2

=65

Here,

r

2

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65

C

2

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Distance between the centre of two circles-

C

1

C

2

=

(3−1)

2

+(8−

2

9

)

2

C

1

C

2

=

4+

4

49

=

2

65

∣r

2

−r

1

∣=

∣

∣

∣

∣

∣

∣

65

−

2

65

∣

∣

∣

∣

∣

∣

=

2

65

∵C

1

C

2

=∣r

1

−r

2

∣

Thus the two circles touches each other internally.

Since the circle touches each other internally. The point of contact P divides C

1

C

2

externally in the ratio r

1

:r

2

, i.e.,

2

65

:

65

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Therefore, coordinates of P are-

⎝

⎜

⎜

⎜

⎜

⎜

⎛

1−2

1(1)−2(3)

,

1−2

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2

9

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⎠

⎟

⎟

⎟

⎟

⎟

⎞

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1

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2

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2

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2

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