Alternate interior angles theorem.
<u>Step-by-step explanation:</u>
By using the definition of Alternate Interior Angles theorem, we can say that If a transversal cuts any two parallel lines, then those pairs of alternate interior angles are seems to be congruent.
So in the given triangle,
∠4 ≅ ∠2
∠5 ≅ ∠3
Sum of all the angles in a triangle = 180°
∠1 + ∠2 + ∠3 = 180°
Since from the above congruence, we can write that
∠1 + ∠4 + ∠5 = 180°
Hence proved.
Answer:
x>1 and y>1
Step-by-step explanation:
x+y>2....... (i)
2x-y>1...... (ii)
Adding equations (i) and (ii),
x+y+2x-y>2+1
3x>3
x>3/3
x>1.
Putting the value of x in equation (i),
1+y>2
y>2-1
y>1.
Answer:
Step-by-step explanation:
∠ACB and ∠ECD are vertical angles, so ∠ACB = ∠ECD.
∠D = ∠B
∠A = ∠E
△ABC and △EDC are similar because they have the same angles.
Answer:
a) = 4.5
b) = 3.3
Step-by-step explanation:
Before solving our problems given to us let us under stand the rule of cube roots
It says ![\sqrt[3]{x \times x \times x} = x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%20%5Ctimes%20x%20%5Ctimes%20x%7D%20%3D%20x)
-----(A)
Also
![\sqrt[3]{x \times x \times x \times y \times y \times y} = x \times y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%20%5Ctimes%20x%20%5Ctimes%20x%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%7D%20%3D%20x%20%5Ctimes%20y)
---(B)
Now let us see each part one by one
a) we have
![\sqrt[3]{64} + \sqrt[3]{0.027} + \sqrt[3]{0.008}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B64%7D%20%2B%20%5Csqrt%5B3%5D%7B0.027%7D%20%2B%20%5Csqrt%5B3%5D%7B0.008%7D)
Now 64 = 4 x 4 x 4
0.027 = 0.3 x 0.3 x 0.3
0.008 = 0.2 x 0.2 x 0.2
substituting these values
![\sqrt[3]{4 \times 4 \times 4} + \sqrt[3]{0.3 \times 0.3 \times 0.3} + \sqrt[3]{0.2 \times 0.2 \times 0.2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%20%5Ctimes%204%20%5Ctimes%204%7D%20%2B%20%5Csqrt%5B3%5D%7B0.3%20%5Ctimes%200.3%20%5Ctimes%200.3%7D%20%2B%20%5Csqrt%5B3%5D%7B0.2%20%5Ctimes%200.2%20%5Ctimes%200.2%7D)
Applying Rule A in above
4.5
b) we have ![\sqrt[3]{0.3 \times 0.3 \times 0.3 \times 11 \times 11 \times 11}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.3%20%5Ctimes%200.3%20%5Ctimes%200.3%20%5Ctimes%2011%20%5Ctimes%2011%20%5Ctimes%2011%7D)
Applying the B rule in this
3.3
Answer:
B is your answer
Step-by-step explanation:
have a great day!
mark me brainliest to be happy
