Given that lines a and b are parallel and that m∠6 = 74°, find m∠1

m∠1 = 106°

Step-by-step explanation:

Here the lines "a" and "b" are parallel and m∠6 = 74°.

We need to find m∠1 .

It is clearly know that from the given information, two parallel lines "a" and "b" cut by a transversal line.

I have attached the figure here. Please have a look at it.

From the figure ∠1 and ∠6 are inside adjacent angles. They add upto 180 degrees.

Therefore, m∠1 + m∠6 = 180°

Given: m∠6 = 74°

So, 74° + m∠1 = 180°

Subtracting 74° from both sides, we get

74° - 74° + m∠1 = 180° - 74°

m∠1 = 106°

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step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15