I'm assuming D is the center of the circle. See the new figure.
Angle BDC = 106 degrees, that's the definition of arc measure.
Triangle BDC is isosceles (two radii make congruent sides) so the two remaining angles in BDC are equal, DBC=DCB=(180-106)/2=37 degrees.
Angle BAC = 106/2 = 53 degrees, subtending the arc of 106 degrees.
Angle CAD = 53/2 = 26.5 degrees because AD is a bisector, the shared hypotenuse of congruent right triangles AED and AFD.
AFD is also congruent to CFD, so angle DCA is also 26.5 degrees
Angle ACB is the sum of DCA and DCB, ACB = 26.5 + 37 = 63.5 degrees
The angle subtends the arc we seek, whose measure must be double:
10x - 23 = 2(63.5) = 127 degrees
10x = 150
x = 15
Answer: 15
Answer:
Step-by-step explanation:
Let the height = h
Let the base = 4h + 7
Area of a triangle = 1/2 * b * h
Area = 93 square inches
1/2 * (4h + 7)* h = 93 Multiply both sides by 2
(4h + 7) * h = 93*2
(4h + 7)*h = 186 Remove the brackets
4h^2 + 7h = 186 Subtract 186 from both sides.
4h^2 + 7h - 186 = 0
Use the quadratic formula to solve
a = 4
b = 7
c = - 186
x1 = (-7 + sqrt(7^2 - 4*4*(-186) ) /2*4
x1 = (-7 + sqrt(49 - 16*(-186)) / 8
x1 = (-7 + sqrt(49 + 2976)) / 8
x1 = (-7 + sqrt(3025)) / 8
x1 = (-7 +55 ) / 8
x1 = (48)/8
x1 = 6
There is another root, but it has to be minus and therefore cannot be used as a length. x2 = - 7.75
h = 6
b = 4*6 + 7 = 31
Check
Area = 1/2 * b * h
Area = 1/2 * 31 * 6
Area = 1/2 *186
Area = 93 which is what we were given so the answer is correct.
Answer: The answer is 43.5 because when using the formula you get this result.
Step-by-step explanation: Area of triangle is base x height divided by 2. So do our base 14.5 and our height 6 and multiply them together. 14.5 x 6 = 87 / 2 = 43.5
D) 36
7 - 3 + 5 = 9 × 4 = 36
