Question

in figure angle ABC=80° find (arc APC)​

Answer 1

in figure angle ABC=80°  (arc APC)​ = 160°

• we use the formula,
• ∠ = 1/2 (arc )
• (The angle subtended by the arc at the center of the circle is twice the angle subtended at any part of the same circle.)
• Given,
• ∠ABC = 80°
• ∴ (arc APC) = 2 ×∠ABC
• = 2× 80°
• = 160 °
• ∴ (arc APC) = 160°

Answer 2

m(arc APC)=160°

Step-by-step explanation:

Angle Inscribed Theorem:

The inscribed angle θ is half of the central angle 2θ that subtends the same arc on the circle.

Given:

In figure angle ABC=80°

To Find

m(arc APC)​

Solution:

By Angle Inscribed Theorem we have,

$m\angle AOC = 2\times m\angle ABC$

Substituting the values we get

$m\angle AOC = 2\times 80=160\°$

Therefore,

$m\angle AOC = m(arc\ APC)=160\°$

Therefore,

m(arc APC)=160°