Matematik för årskurs 7-9/Geometri/Vinklar/Exempel/Beräkna vinkelsummor

Exempel 1:

• In the diagram above, the two lines marked with arrows are parallel. You are given the angle of 56^o and of 115^{o. Find the angle x.}

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Lösning

The angle $\displaystyle \alpha$ is the same as the 56^o angle, since the two lines marked with arrows are parallel and the line that crosses them must cross parallel lines at the same angle.

The angle $\displaystyle \beta$ is 180^o-115^o since it and the 115^o angle add up to a straight line. So it is 65^o.

We can now redraw the diagram with the angles as follows:

We have a triangle with angles x, 56^o and 65^o.

x+56^o+65^o=180^o.

x+121^o=180^o.

x=59^o.

Exempel 2:

• In the diagram above two angles are marked as 75^o and one as 101^o. Find the angle c.

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Lösning

There is an isosceles triangle with angles 75^o, 75^o and an unknown angle b. So

b+75^o+75^o=180^o.

b+150^o=180^o.

b=30^o.

$\displaystyle \angle BAC=101^{\circ }$

The angle 'c' is an angle in triangle $\displaystyle \Delta ABC$. The other two angles are 30^o and 101^o.

c+30^o+101^o=180^o.

c+131^o=180^o.

c= 49^o.