Question

Observe the given figure and complete the following activity to find the measure of an angle in a semicircle.​

Answer 1

Answer:

,1 blank --- AC

2 blank ----AC

3 blank -----90°

4 blank -----90°

Step-by-step explanation:

hope this hlp u!!!!!

Answer 2

Given :- Observe the given figure and complete the following activity to find the measure of an angle in a semicircle.

• seg AC is the diameter .
• m(arc AMC) = 180°

To Find :-

1. ∠ABC = (1/2) m(arc ___)
2. ∠ABC = (1/2) × ____
3. ∠ABC = ______
4. angled inscribed in a semi - circle is a ____

Solution :-

we know that,

• The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle .

since, Diameter AC is a straight line .

so,

→ Angle at centre = 180° (straight line.)

then,

→ Angle inscribed in circle circumference = half of 180°

→ ∠ABC = (1/2) × 180°

→ ∠ABC = 90° .

therefore, we can conclude that,

1) ∠ABC = (1/2) m(arc AMC)

2) ∠ABC = (1/2) × 180°

3) ∠ABC = 90°

4) Angle inscribed in a semi - circle is a right angle .

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