Question

Observe the given figure and complete the following activity to find the

measure of an angle inscribed in a semicircle.

Seg AC is the diameter.

∠ABC is inscribed in a semicircle ABC.



m (arc AMC) =

∠ABC = 1

2

m(arc ) [Inscribed

angle theorem]

\ ∠ABC =

1

2 ×

\ ∠ABC =​

Answer 1

i) ∠ABC = (1/2) m(arc AMC)

ii) ∠ABC = (1/2) × 180°

iii) ∠ABC = 90°

iv) The angled inscribed in a semi-circle is 90° i.e a right-angle

Given:

Observe the given figure

Seg AC is the diameter of a circle

To Find:

Fill in the blanks given

i) ∠ABC = (1/2) m(arc ___)

ii) ∠ABC = (1/2) × ____

iii) ∠ABC = ______

iv) The angled inscribed in a semi-circle is a ____

Solution:

The measure of (arc AMC) = 180°

The angle at the center theorem is another name for the inscribed angle theorem. According to the inscribed angle theorem, the inscribed angle is half of the central angle.

As we know diameter AC is a straight line.

=> The angle at center = 180° (straight line.)

According to the Inscribed angle theorem

An angle inscribed in circle circumference = half of 180°

=> ∠ABC = (1/2) m(arc AMC)

=> ∠ABC = (1/2) × 180°

=> ∠ABC = 90°.

Therefore,  

i) ∠ABC = (1/2) m(arc AMC)

ii) ∠ABC = (1/2) × 180°

iii) ∠ABC = 90°

iv) The angled inscribed in a semi-circle is 90° i.e a right-angle

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Complete Question:

Answer 2

The measure of (arc AMC) = 180°

The angle at the center theorem is another name for the inscribed angle theorem. According to the inscribed angle theorem, the inscribed angle is half of the central angle.

As we know diameter AC is a straight line.

=> The angle at center = 180° (straight line.)

According to the Inscribed angle theorem

An angle inscribed in circle circumference = half of 180°

=> ∠ABC = (1/2) m(arc AMC)

=> ∠ABC = (1/2) × 180°

=> ∠ABC = 90°.

Therefore,  

i) ∠ABC = (1/2) m(arc AMC)

ii) ∠ABC = (1/2) × 180°

iii) ∠ABC = 90°

iv) The angled inscribed in a semi-circle is 90° i.e a right-angle