Answer:
∠ DAB = 48°
Step-by-step explanation:
The sum of the 3 angles in Δ ACD = 180° , then
∠ CAD + 60° + 90° = 180° , that is
∠ CAD + 150° = 180° ( subtract 150° from both sides )
∠ CAD = 30°
Then
∠ DAB + ∠ CAD = ∠ CAB
∠ DAB + 30° = 78° ( subtract 30° from both sides )
∠ DAB = 48°
Answer:
Step-by-step explanation:
Step-by-step explanation:
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Answer:
A) 3/4
Step-by-step explanation:
Given: Both circle A and circle B have a central angle measuring 50°.
The area of circle A's sector is 36π cm2.
The area of circle B's sector is 64π cm2.
We know, area of the circle= ![\pi r^{2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D)
lets assume the radius of circle A be "
" and radius of circle B be "
"
As given, Area of circle A and B´s sector is 36π and 64π repectively.
Now, writing ratio of area of circle A and B, to find the ratio of radius.
⇒![\frac{\pi r_1^{2} }{\pi r_2^{2} } = \frac{36\pi }{64\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20r_1%5E%7B2%7D%20%20%7D%7B%5Cpi%20r_2%5E%7B2%7D%20%7D%20%20%3D%20%5Cfrac%7B36%5Cpi%20%7D%7B64%5Cpi%20%7D)
Cancelling out the common factor
⇒ ![\frac{r_1^{2} }{r_2^{2} } = \frac{36 }{64}](https://tex.z-dn.net/?f=%5Cfrac%7Br_1%5E%7B2%7D%20%20%7D%7Br_2%5E%7B2%7D%20%7D%20%20%3D%20%5Cfrac%7B36%20%7D%7B64%7D)
⇒ ![(\frac{r_1 }{r_2} )^{2} = \frac{36 }{64}](https://tex.z-dn.net/?f=%28%5Cfrac%7Br_1%20%20%7D%7Br_2%7D%20%29%5E%7B2%7D%20%3D%20%5Cfrac%7B36%20%7D%7B64%7D)
Taking square on both side.
Remember; √a²= a
⇒ ![(\frac{r_1 }{r_2} ) =\sqrt{ \frac{36 }{64}}](https://tex.z-dn.net/?f=%28%5Cfrac%7Br_1%20%20%7D%7Br_2%7D%20%29%20%3D%5Csqrt%7B%20%5Cfrac%7B36%20%7D%7B64%7D%7D)
⇒ ![(\frac{r_1 }{r_2} ) = \frac{6}{8}](https://tex.z-dn.net/?f=%28%5Cfrac%7Br_1%20%20%7D%7Br_2%7D%20%29%20%3D%20%5Cfrac%7B6%7D%7B8%7D)
⇒![\frac{r_1 }{r_2} = \frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Br_1%20%20%7D%7Br_2%7D%20%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
Hence, ratio of the radius of circle A to the radius of circle B is 3:4 or 3/4.
Answer: 47 degrees
Step-by-step explanation:
7x-9=4x+15 because of the vertical angle rule
7x-9=4x+15
3x=24
x= 8
So the angle 7(8)-9 = 47°