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If M is the midpoint of triangle ABC, ACB = 30degrees and BMA = 45 degrees, calculate the size of BAC in degrees.

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  • paulgbrandon Jun 06, 2017

    Hi fazlurahman , I want to help you with your question, but I need more information from you. Can you please add details in the comment box? Please clarify what you mean by the midpoint of the triangle.

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It would be better if you send us also an image of the triangle since it's quite unclear from your message whether the midpoint is created by straight line AM or BM . anyways you can always get help from the website i get my algebra homework help

Posted on Oct 17, 2017

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30 degrees

Posted on Sep 30, 2017

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Since M is the mid point of the triangle, the distance of M from A,B and C is equal which means AM = BM = CM.
Therefore, MAB = MBA. In triangle MAB, MAB=45 degrees.
sum of angles in a triangle = 180 deg. So, sum of angles MAB and MBA = 180 - BMA = 180 -45 = 135.
Since both MAB and MBA are equal , MAB = 135/2 = 67.5
In triangle AMC, MAC = MCA . Therefore MAC = 30/2 = 15 deg.
Therefore total BAC = MAC + MAB =82.5 deg.

Posted on Sep 30, 2017

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Posted on Jan 02, 2017

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1 Answer

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-----------
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1 Answer

How many sides does a regular polygon have when the interior degrees is 176?


Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.
(n-2)180 = 176
-----------
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Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

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Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

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