Mathematics: Due rn for a test help

Due rn for a test help - id14865407, benallyadam2067

Ответ:

Maddifalls1562

16.10.2020

$m\angle WVT=40^{\circ}$

Step-by-step explanation:

When two secants or a secant and a tangent of a circle intersect outside the circle, the measure of the acute angle formed is equal to half of the positive difference of smaller and larger arc formed.

Therefore, we have the equation:

$m\angle WVT=\frac{1}{2}(\widehat{TW}-\widehat{UW}),\\3x+4=\frac{1}{2}(14x+7-(7x+11))$

Distribute:

$3x+4=\frac{1}{2}(14x+7-7x-11),\\\\3x+4=\frac{1}{2}(7x-4),\\\\3x+4=3.5x-2$

Add 2 to both sides and subtract from both sides:

6=0.5x

Divide both sides by 1/2:

$x=\frac{6}{\frac{1}{2}}=6\cdot 2=12$

Now substitute x=12 into 3x+4 :

$m\angle WVT=3(12)+4,\\m\angle WVT=36+4,\\m\angle WVT=\boxed{40^{\circ}}$

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