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3 years ago

In circle K, what is the value of x?

Mathematics

1 answer:

djyliett [7]3 years ago

8 0

Answer:

18°

Step-by-step explanation:

A diameter cuts a circle into two arcs that are each 180°. An inscribed angle that intercepts an arc of 180° has a measure of 90°. Thus we have ...

... 5x = 90°

.. 90°/5 = x = 18°

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allsm [11]

Answer:

m∠DEC = 78°

Step-by-step explanation:

Given information: AC = AD, AB⊥BD, m∠DAC = 44° and CE bisects ∠ACD.

If two sides of a triangles are congruent then the opposite angles of congruent sides are congruent.

AC = AD (Given)

$\angle ADC\cong \angle ACD$

$m\angle ADC=m\angle ACD$

According to the angle sum property, the sum of interior angles of a triangle is 180°.

$m\angle ADC+m\angle ACD+m\angle DAC=180$

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$2m\angle ACD=180-44$

$2m\angle ACD=136$

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$m\angle ACD=68$

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$m\angle ACE=m\angle DCE=\dfrac{\angle ACD}{2}$

$m\angle ACE=m\angle DCE=\dfrac{68}{2}$

$m\angle ACE=m\angle DCE=34$

Use angle sum property in triangle CDE,

$m\angle CDE+m\angle DCE+m\angle DEC=180$

$68+34+m\angle DEC=180$

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Subtract 102 from both sides.

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Therefore, the measure of angle DEC is 78°.

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