The circle illustrates the theorems of angles in the same segment
- The measure of angle NTS is 53°
- The measure of arc AB is 200°
How to determine the measure of NTS?
Given that:
∠SKA = 74°
The angle SKA is at the center of the circle.
This means that:
Arc AS = 74°
Calculate Arc SN using:
SN + AS = 180°
Substitute 74 for AS
SN + 74° = 180°
Subtract 74 from both sides
SN = 106°
The arc SN is subtended by the angle NTS.
This means that:
∠NTS = 0.5 * SN
So, we have:
∠NTS = 0.5 * 106°
Evaluate
∠NTS = 53°
Hence, the measure of angle NTS is 53°
How to determine the measure of arc AB?
Given that:
∠BCA = (7w - 4)°
∠ADB = (5w + 20)°
Angles subtended by the same arc at the circumference are congruent.
So, we have:
7w - 4 = 5w + 20
Collect like terms
7w - 5w = 20 + 4
Evaluate
2w = 24
Divide by 2
w = 12
This implies that:
∠BCA = (7 * 12 - 4)°
Evaluate
∠BCA = 80°
The measure of arc AB is then calculated using:
AB = 360 - 2 * ∠BCA
This gives
AB = 360 - 2 * 80°
Evaluate
AB = 200°
Hence, the measure of arc AB is 200°
Read more about arcs and segments at:
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