Question

It is hard to find please help me.​

Answer 1

Question

AB is a diameter of a circle, centre O. C is a point on the circumference of a circle, such that ∠CAB = 2 x ∠CBA. Find ∠CBA.

Given

• AB is a diameter.
• C is a point on the circumference.
• ∠CAB = 2 x ∠CBA

To Find

• ∠CBA

Step by step explanation

• AB is a Diameter.
• C is a point on the circumference.

$\mathfrak{as \: we \: know \: that}$

$\sf \: The ~angle ~at ~the~ circumference~ in~ a~ semicircle~ is~ a~ right ~angle.$

∠ACB= 90⁰

Let, ∠CBA=x

then, ∠CAB = 2x

$\sf \: →∠ACB+∠CBA+∠CAB = 180⁰ \: \: \: \: \: \pink{angle \: sum \: property}$

$\sf→90°+3x=180°$

$\sf→3x=90$

$~~~~~~~\sf x=30$

$\sf∠CBA=30⁰$

$\sf∠CAB = 2×30°$

⁣$~~~~~~~~~~~\underline{\boxed{\sf{∠CAB = 30°}}}$