What is the measure of angle z in this figure?

Mathematics

1 answer:

astraxan [27]3 years ago

3 0

Hello!

I've attached a photo for reference.

Lines A and B form straight angles, which measure 180 degrees. That means that -

m∠x + m∠y = 180°
m∠y + m∠z = 180°
m∠z + 43° = 180°
43° + m∠x = 180°

Since you're trying to find z, use the solvable equation with z in it:

m∠z + 43° = 180°
180 = z + 43
137 = z

Answer:
m∠z = 137°

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What is the length of the tangent line in the picture?

S_A_V [24]

Answer:

x = -2

Step-by-step explanation:

The tangent line has length "x + 8"

The secant line has length "x + 6 + 5", where

5 is the inner part

x + 6 is the outer part

Now,

the secant-tangent theorem tells us that square of the tangent line is equal to the outer segment of secant line multiplied by length of whole secant line.

So, we can say:

$(x+8)^2 = (x+6)(x+6+5)$