Question

If AB and DE are equal chords & OC and OQ are perpendicular to AB AND DE respectively. Then find the value of ANGLE ACQ.


Don't Spam ⚠️⚠️⚠️⚠️

Need Full explanation...

Answer should be 75°​

Answer 1

Answer

$\sf{\angle{ACQ}\:=\:75^{\circ}}$

Explanation

Given that, AB and DE are equal chords & OC and OQ are perpendicular to AB and DE respectively.

OC is a chord perpendicular to AB from a centre O.

Similarly, OQ is a chord perpendicular to DE from a centre O.

Given that opposite sides AB and DE are equal chords. Then, their corresponding angles i.e. angle OCQ and angle OQC are also equal.

$\implies\:\sf{\angle{1}\:=\:\angle{2}}$

In ∆OCQ

By angle sum property

Sum of all angles of triangles is 180°.

→ $\sf{\angle{1}+\angle{2}+\angle{O}\:=\:180^{\circ}}$

→ $\sf{\angle{1}+\angle{1}+150^{\circ}\:=\:180^{\circ}}$

→ $\sf{2\angle{1}\:=\:180^{\circ}-150^{\circ}}$

→ $\sf{2\angle{1}\:=\:30^{\circ}}$

→ $\sf{\angle{1}\:=\:15^{\circ}}$

So,

$\sf{\angle{1}\:=\:\angle{2}\:=\:15^{\circ}}$

Now,

$\rightarrow\:\sf{\angle{OCB}+\angle{OCQ}+\angle{ACQ}\:=\:180^{\circ}}$

Substitute the known values above. To find the angle ACQ.

$\rightarrow\:\sf{90^{\circ}+15^{\circ}+\angle{ACQ}\:=\:180^{\circ}}$

$\rightarrow\:\sf{105^{\circ}+\angle{ACQ}\:=\:180^{\circ}}$

$\rightarrow\:\sf{\angle{ACQ}\:=\:180^{\circ}-150^{\circ}}$

$\rightarrow\:\sf{\angle{ACQ}\:=\:75^{\circ}}$

Answer 2

75° is the answer

Hope it helps you ✌