circle E with a diameter AC and m<DAC = 62 degrees, calculate the following
m<BAC arc m<AD m<ABD and m<DBC
No idea where B is.
arc length is radius time central angle.
m<DEC = 2*m<DAC
m<DEA = 180 - m<DEC = 180-124 = 56
arc AD = radius * 56 = AC*28*(pi/180)
To solve this problem, we can use the properties of angles and arcs in a circle.
1. m<BAC:
The angle at the center of a circle is twice the angle at the circumference that subtends the same arc. Since angle DAC is given as 62 degrees and it subtends arc AC, we can say that arc AC = 62 degrees. Since arc AC is the entire circle, the angle at the center is 2 times the angle at the circumference, so m<BAC = 2 * arc AC = 2 * 62 = 124 degrees.
2. arc m<AD:
We know that angle DAC is given as 62 degrees. The arc m<AD is the arc between points A and D on the circle. Since the diameter AC passes through the center of the circle, arc m<AD is half of the circle. Therefore, arc m<AD = 0.5 * 360 degrees = 180 degrees.
3. m<ABD:
Since triangle ADB is inscribed in circle E, angle ABD is half the measure of the arc AD. From part 2, we know that arc AD is 180 degrees. Therefore, m<ABD = 0.5 * arc AD = 0.5 * 180 = 90 degrees.
4. m<DBC:
Angle DBC is an angle formed between the diameter AC and the tangent BC. In a circle, a tangent is perpendicular to the radius at the point of contact. Therefore, angle DBC is a right angle, which means m<DBC = 90 degrees.
To summarize:
m<BAC = 124 degrees
arc m<AD = 180 degrees
m<ABD = 90 degrees
m<DBC = 90 degrees