Please asnerw this pic attached below

Mathematics

1 answer:

mamaluj [8]3 years ago

8 0

Answer:

x = 30

Step-by-step explanation:

Look at triangle LMN.

m<NLM + m<M + m<MNL = 180

90 + m<M + 45 = 180

m<M = 45

Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

<ONM is an exterior angle of triangle KMN.

The remote interior angles are <K and <M.

m<K + m<M = m<ONM

2x + 45 = 105

2x = 60

x = 30

Answer: x = 30

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jeka57 [31]

Answer:

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Step-by-step explanation:

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3 years ago

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zloy xaker [14]

Answer: see proof below

Step-by-step explanation:

Given: A + B + C = 90° → A + B = 90° - C

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Use the Double Angle Identity: cos 2A = 1 - 2 sin² A

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$\text{Double Angle:}\qquad \dfrac{1-\cos 2A}{2}+\dfrac{1-\cos 2B}{2}+\sin^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2-\cos 2A-\cos 2B\bigg)+\sin^2 C\\\\\\.\qquad \qquad \qquad =1-\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\sin^2 C$

$\text{Sum to Product:}\quad 1-\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\sin^2 C\\\\\\.\qquad \qquad \qquad =1-\cos (A+B)\cdot \cos (A-B)+\sin^2 C$