C. Acute vertically opposite angles
Sum would be equal to 720.
so, x-60 + x-40 + 130 + 120 + 110 + x-20 = 720
3x + 240 = 720
3x = 720 - 240
x = 480/3
x = 160
Angle F = x-20 = 160 - 20 = 140
In short, Your Answer would be 140
Hope this helps!
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
True
Step-by-step explanation:
The hypothesis of a conditional statement is the "if" part. This means the hypothesis is "If a line is bisected."
The conclusion of a conditional statement is the "then" part. This means the conclusion is "then it is cut into two equal parts."
1/2 (Base x height) = area
1/2 (4*x)=10
2x=10
X=5
The height is 5 units
