Question

In the diagram shown, what’s the measure of

Answer 1

m∠BAC = 40°

Explanation:

In a triangle, the sum of the internal angle is equal to the sum of the external angles opposite to them. So taking that into account we can say that:

(2x + 2) + (4x + 8) = 8x - 30

Get rid of the parentheses:

2x + 2 + 4x + 8 = 8x - 30

Combine like terms:

6x + 10 = 8x - 30

Subtract 30 from both sides of the equation:

6x + 10 - 10 = 8x - 30 - 10

6x = 8x - 40

Subtract 8x from both sides of the equation"

6x - 8x = 8x - 8x - 40

-2x = -40

Then divide both sides by -2

-2x/-2 = -40/-2

x = 20

So now that we know x, we can solve for the m∠BAC

m∠BAC = 2x + 2

m∠BAC = 2(20) + 2

m∠BAC = 40 + 2

m∠BAC = 40°