# How is the angle same in friction force? [closed]

How is the angle $$\theta$$ of the plane and between the $$mg$$ (attraction due to gravity) and component of $$mg$$ is same?

In the figure $$\theta$$ between the $$mg$$ and its component $$mg\cos\theta$$ is same as the angle between the horizontal surface and the inclined plane. How?

## closed as off-topic by stafusa, John Rennie, Jon Custer, tpg2114♦Aug 12 at 17:33

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• "Angle between two lines is same as angle between their normals" – HS Singh Aug 11 at 5:52
• Thanks, i didn't know that. – Dujana Abrar Aug 11 at 5:59
• This should be something proved in a geometry class – Kyle Kanos Aug 11 at 11:29

The triangle between the horizontal, the slope, and the downward gravitational component is a right angle composed of the angles $$\theta,90,$$ and $$90-\theta$$, with the $$90-\theta$$ angle occurring in the top right corner. Because that angle forms a 90 degree angle with the angle in question, then the unknown angle ($$\phi$$) must be $$90-90+\theta = \theta$$.
The triangle made by the incline, ground and mg AND the triangle made by mg , mg cos $$\theta$$, and the dash line connecting these two vectors are similar.