Find M Please help!!!! Last question worth 10 points!

Mathematics

1 answer:

Alecsey [184]2 years ago

6 0

Answer:

<A = 75degrees

Step-by-step explanation:

From the triangle given;

arcDA + arc AD + arcBD = 360 degrees

131 + 79 + arcBD = 360

210 + arcBD = 360

arcBD = 360 -210

arcBD = 150 degrees

Since the angle at the vertex <A is half that at the arc BD, hence;

<A = 1/2 arcBD

<A = 1/2 * 150

<A = 75degrees

Hence the measure of angle A s 75degrees

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Please help! 30 points!

Rashid [163]

Answer: $64.2^{\circ}$

Step-by-step explanation:

According to the cosine rule

$\cos C=\dfrac{a^2+b^2-c^2}{2ab}$

Here, $a=83, b=111, c=165,\ C=180^{\circ}-\theta$

Putting values

$\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}$