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How do you solve this ?

How do you solve this ?-example-1
User YounesM
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1 Answer

19 votes
19 votes

Explanation:

first of all, remember for life :

the sum of all angles in a triangle is always 180°.

so, in this right-angled triangle we have therefore

180 = b + 90 + 71

b = 180 - 90 - 71 = 19°

and then regarding a and b :

the sum of all angles around a single point on one side of a line is also always 180°.

why ? because the line can be seen as the extended diameter of a circle, with that point being the center of the circle. and one side of the line is representing half of that circle. and a half-circle is 180°.

so,

a + b = 180

a + 19 = 180

a = 180 - 19 = 161°

FYI, the reason for the first principle (all angles in a triangle are together 180°) is also based on a half-circle concept : any right-angled triangle can be seen as inscribed into a half-circle, with the Hypotenuse (the baseline opposite of the 90° angle) being the diameter of the circle, and the center of the circle being the midpoint of the Hypotenuse.

User Way
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