SOLUTION: If the measures of the exterior angles of the acute angles of a right triangle are 2x+15 and 3x+5, find the measures of the acute angles.

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Question 768339: If the measures of the exterior angles of the acute angles of a right triangle are 2x+15 and 3x+5, find the measures of the acute angles.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!


If the measures of the exterior angles of the acute angles of a right triangle are 2x+15 and 3x+5, find the measures of the acute angles.

Ans:

Remember that the sum of the angle + the exterior angle is 180.

Also that the sum of the 3 angles of the triangle is 180. In the right triangle,

since one angle is 90, the sum of the other 2 acute angles is 90 as well.



If the 2 acute angles are A and B,

A+%2B+2%2Ax+%2B+15+=+180

A+=+180+-+%282%2Ax+%2B+15%29+=+165+-+2%2Ax

Similarly,

B+%2B+3%2Ax+%2B+5+=+180

So B+=+180+-+%283%2Ax+%2B+5%29+=+175+-+3%2Ax



A + B = 90

So, 165+-+2%2Ax+%2B+175+-+3%2Ax+=+90

Combining like terms,

340+-+5%2Ax+=+90

340+-+90+=+250+=+5%2Ax

x+=+50

So the first acute angle A = 165+-+2%2Ax = 165+-+100 = highlight%2865%29

The second acute angle B = 175+-+3%2Ax = 175+-+150 = highlight%2825%29



Hope you got it :)