Answer:
The answer is 75 degrees.
Step-by-step explanation:
The explanation is that the the supplementary angle to 80 is 100 since a straight line has an angle of 180, now the 100 degree angle is congruent to the angle x + 25 which means that x + 25 is equal to 100 so x is 75
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:
1,546 ≈ 2,000
Hope this helps :)
1. To round to nearest thousands, first look at the hundreds place if the number is 1,2,3,4 then round down. If the number is 5,6,7,8,9 then round up.
Step-by-step explanation:
1.3×2×a×b
=6ab
2.c5×c
=c5+1
=c6
3.2y4×5y3
=10y4+3
=10y7
4.3gh2×4g3h3
=12g1+3h2+3
=12g4h5
