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In a triangle, the measure of the middle angle
is triple the measure of the smallest angle, and
the measure of the largest angle is 55° greater
than the measure of the smallest angle. Find
the measures of the
angles.

Respuesta :

LadyStrange

Let the smallest angle in a triangle be = x

Largest angle in a triangle = 55 + x

The middle angle in a triangle = 3x ( triple the measure of the smallest angle )

Their sum = 180° ( according to the angle sum property all the angles of a triangle sum up to 180° )

This can be written as :

= x + 55 + × + 3x = 180

Let us find each angle by solving the equation .

= x + 55 + x + 3x = 180°

= x + x + 3x + 55 = 180°

= 5x + 55 = 180°

= 5x = 180 - 55 ( transposing +55 from LHS to RHS changes +55 to -55 )

= 5x = 125

= x = 125 ÷ 5 (transposing ×5 from LHS to RHS changes ×5 to ÷5 )

= x = 25

Using this let us find the measure of each angle .

Smallest angle = x = 25

Smallest angle = 25°

Middle angle = 3x = 3 × 25 = 75

Middle angle = 75°

The largest angle = x + 55 = 25 + 55 = 80

Largest angle = 80°

Therefore , the measure of the smallest angle = 25° , the measure of the middle angle = 75° and the measure of the largest angle = 80° .

okpalawalter8

We have that the measures of the  angles are as follows

[tex]\theta_1=80 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

[tex]\theta_3=25 \textdegree[/tex]

From the question we are told that:

The measure of the middle angle  is triple the measure of the smallest angle

The measure of the largest angle is 55° greater  than the measure of the smallest angle

Let

[tex]\theta_1=Largest\ angle[/tex]

[tex]\theta_2=Middle\ angle[/tex]

[tex]\theta_3=Smallest\ angle[/tex]

Therefore

[tex]\theta_1=55 \textdegree+\theta_3\\\\\theta_2=3*\theta_3[/tex]

Generally, the equation for the angle of a triangle is mathematically given by

[tex]\theta_1+\theta_2+\theta_3=180[/tex]

Therefore

[tex]55 \textdegree+\theta_3+3*\theta_3+\theta_3=180[/tex]

[tex]\theta_3=25 \textdegree[/tex]

Therefore

Substitute [tex]\theta_3[/tex] into equations of [tex]\theta_1[/tex] and [tex]\theta_2[/tex]

For [tex]\theta_1[/tex]

[tex]\theta_1=55 \textdegree+25 \textdegree\\\\\theta_1=80 \textdegree[/tex]

For [tex]\theta_2[/tex]

[tex]\theta_2=3*\theta_3[/tex]

[tex]\theta_2=3*25 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

in conclusion

The measures of the  angles are as follows

[tex]\theta_1=80 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

[tex]\theta_3=25 \textdegree[/tex]

For more information on this visit

https://brainly.com/question/17581080

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