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KonstantinChe [14]
2 years ago
13

Find the value of X and prove the following​

Mathematics
2 answers:
Goshia [24]2 years ago
6 0

Answer:

In △AXY and △ABC

∠XAY=∠BAC (Common angle)

∠AXY=∠ABC (Corresponding angles for parallel lines XY and BC)

∠AYX=∠ACB (Corresponding angles for parallel lines XY and BC)

Thus, △AXY∼△ABC (AAA rule)

Hence,

AB/AX = AY/AC = XY/BC

(Corresponding sides)

3+1.5/3 = XY/6

XY= 4.5/3×6

XY=4cm

natali 33 [55]2 years ago
5 0

The value of the variable <em>x</em> can be determined using the circle theorem to

determine the angle formed by <em>x</em>.

The correct responses are;

  • (1) x = <u>30°</u>
  • (2) x = <u>100°</u>
  • (3) x = <u>60°</u>

Reasons:

(1) From circle theorem, we have;

  • Equal chords subtends equal arcs and vice versa
  • Equal chords subtend equal angles at the center of a circle

Therefore;

Angle subtended by \displaystyle \widehat {AB} at center = Angle subtended by \widehat {BC} at the center;

  • Angle at the center = 2 × Angle at the circumference

Therefore;

Angle subtended by \displaystyle \widehat {AB} at the circumference = Angle subtended by \mathbf{\widehat {BC}} at the circumference

Which gives;

  • x = <u>30°</u>

(2) \displaystyle \widehat {AB} = \mathbf{\widehat {CD}} given

Angle subtended by arc \widehat {CD} at the center = x

Equal arcs subtend equal angles at the center of a circle.

Therefore;

Angle subtended by arc \mathbf{\widehat {AB}} at the center = x

Angle at center = 2 × angle at circumference

Therefore;

x = 2 × 50° = 100°

x = <u>100°</u>

(3) \displaystyle \widehat {AC} = \mathbf{ 3 \times \widehat {AB}} given

By definition, we have;

Angle subtended by \widehat {AC} at the center = 3 × Angle subtended by \widehat {AB} at the center

According to circle theorem, we have;

Angle at the center = 2 × Angle at the circumference

Let <em>y</em> represent the angle subtended at the circumference by \widehat {AB}, we have;

y = 20°

\widehat {AB} = 2·y

\widehat {AC} = 3 × \widehat {AB} = 3 × 2·y = 6·y

Therefore;

\widehat {AC} = 6 × 20° = 120°

\widehat {AC} = 120°

\widehat {AC} = 2·x

Therefore;

2·x = 120°

\displaystyle x = \frac{120^{\circ}}{2} = \mathbf{ 60^{\circ}}

x = <u>60°</u>

Learn more circle theorems here:

brainly.com/question/16879446

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