Question

Find the values of​ x, y, and z in the triangle to the right. A triangle has angles labeled as follows: lower left, x degrees; top, y degrees; lower right, z degrees. A ray extends the left side of the triangle and the angles labeled y degrees and (3 x plus 5) degrees form a straight angle. Another ray extends the bottom side of the triangle and the angles labeled z degrees and (3 x minus 5) degrees form a straight angle. X degrees y degrees z degrees left parenthesis 3 x plus 5 right parenthesis degrees left parenthesis 3 x minus 5 right parenthesis degrees

Answer 1

Given:

Consider the below figure attached with this question.

Angles of a triangle are x, y and z.

To find:

The values of x, y and z.

Solution:

If two angles are linear pair, then their sum is 180 degrees.

$y+(3x+5)=180$

$y=180-3x-5$

$y=175-3x$

Similarly,

$z+(3x-5)=180$

$z=180-3x+5$

$z=185-3x$

According the the angle sum property, the sum of all angles of a triangle is 180 degrees.

$x+y+z=180$

$x+(175-3x)+(185-3x)=180$

$-5x+360=180$

$-5x=180-360$

$-5x=-180$

Divide both sides by -5.

$x=36$

The value of x is 36.

$y=175-3(36)$

$y=175-(108)$

$y=67$

Now,

$z=185-3(36)$

$z=185-108$

$z=77$

Therefore, the values of x, y and z are 36, 67 and 77 respectively.