Answer:
N:10
Step-by-step explanation:
What are the answer choices
Answer:
The measure of arc BC is 130° ⇒ 1st answer
Step-by-step explanation:
In a circle:
- The measure of an arc is equal to the measure of the central angle subtended by it
- The measure of an arc is equal to double the measure of the inscribed angle subtended by it
- Central angles subtended by the same arc are equal in measures
- Inscribed angles subtended by the same arc are equal in measures
- The measure of central angle is double the measure of the inscribed angle which subtended by its arc
∵ Angle BDC is an inscribed angle
∵ It is subtended by the arc BC
- By using the 2nd fact above
∴ The measure of arc BC = 2 × the measure of ∠BDC
∵ The measure of angle BDC is 65 degree
∴ The measure of arc BC = 2 × 65°
∴ The measure of arc BC = 130°
The measure of arc BC is 130°
Answer:
Step-by-step explanation: Since the given problem states that the two angles, angle 1 and angle 2 form a linear pair, this means that they form a 180° line, so that:
measure angle 1 + measure angle 2 = 180°
Since measure of angle 2 is six more than twice the measure of angle 1, therefore:
measure angle 2 = 2 (measure angle 1) + 6
hence, substituting this into the first equation:
measure angle 1 + 2 (measure angle 1) + 6 = 180
3 (measure angle 1) = 174
measure angle 1 = 58°
Therefore,
measure angle 2 = 2 (measure angle 1) + 6
measure angle 2 = 2 (58°) + 6
measure angle 2 = 122*