Answer:
65°
Step-by-step explanation:
Radii CA and CB are perpendicular to tangent lines AT and BT, so

Since angle BAT is equal to 65°, angle CAB has measure

Consider triangle ACB. This triangle is isosceles, because CA=CB as radii of the circle. Two angles adjacent to the base are congruent, thus

The sum of the measures of all interior angles in triangle is always 180°, so

Angle ACB is central angle subtended on the minor arc AB, angle APB is inscribed angle subtended on the same minor arc AB. The measure of inscribed angle is half the measure of central angle subtended on the same arc, so

Answer:
60°
please look into the solution down here.
Step-by-step explanation:
since BD bisects it, then the angles should be bisected symmetrically, or in other words, ANGLE ABD = angle DBC,
hence,
4x = 2x +30
2x = 30
x = 15
therefore, angle DBC = 2x + 30 = 2(15) + 30 = 60°.
Answer:
its a little too small
Step-by-step explanation:
The angle is a complementary angle so both angles add up to 90 degrees
Therefore set your equation equal to 90 to find angle of x
53+x=90
Subtract 53 from both sides
X= 37 degrees
<h3>
Answer: A. 9</h3>
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Explanation:
Draw in the segments AO and OC.
Triangle ABO is congruent to triangle CBO. We can prove this through the use of the HL theorem. HL stands for hypotenuse leg.
Since the triangles are congruent, this means the corresponding pieces AB and BC are the same length.
Then we can say:
AB+BC = AC .... segment addition postulate
AB+AB = AC .... plug in BC = AB
2*AB = AC
2*AB = 18
AB = 18/2 .... divide both sides by 2
AB = 9
In short, the chord AC is bisected by the perpendicular radius drawn in the diagram. So all we do is cut AC = 18 in half to get AB = 9.