You can observe that angle 1 and angle with 47° are inside a parallelogram.
Consider that the sum of the internal angles of a parallelogram is 360°.
Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.
Consider that angle down right side is congruent with angle 1, then, they have the same measure.
You can write the previous situation in the following equation:
47 + 47 + ∠1 + ∠1 = 360 simplify like terms
94 + 2∠1 = 360 subtract both sides by 94
2∠1 = 360 - 94
2∠1 = 266 divide by 2 both sides
∠1 = 266/2
∠1 = 133
Hence, the measure of angle 1 is m∠1 = 133°
Answer:
50.24m²
Step-by-step explanation:
area of circle
= 3.14 × r²
= 3.14 × 4 × 4
= 50.24
Answer: 105.84 cm^2
To find the answer, first you have to start by finding the percent of the circle in the sector. Convert the radians given to 108 degrees. 108 out of 360 is 30%.
Now, find the area of the circle. It's pi x r^2, so the area is 352.810.
Multiply this by 30% to find our area of 105.84 cm^2
Answer:
Step-by-step explanation:
10) The opposite sides of a parallelogram are equal. It means that
a + 15 = 3a + 11
3a - a = 15 - 11
2a = 4
a = 4/2 = 2
Also,
3b + 5 = b + 11
3b - b = 11 - 5
2b = 4
b = 4/2 = 2
11) The opposite angles of a parallelogram are congruent and the adjacent angles are supplementary. This means that
2x + 11 + x - 5 = 180
3x + 6 = 180
3x = 180 - 6 = 174
x = 174/3 = 58
Therefore,
2x + 11 = 2×58 + 11 = 127 degrees
The opposite angles of a parallelogram are congruent, therefore,
2y = 127
y = 127/2 = 63.5
12) The diagonals of a parallelogram bisect each other. This means that each diagonal is divided equally at the midpoint. Therefore
3y - 5 = y + 5
3y - y = 5 + 5
2y = 10
y = 10/2 = 5
Also,
z + 9 = 2z + 7
2z - z = 9 - 7
z = 2