Mathematics, 16.10.2020 15:01 Jonah58

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.

Answers: 1

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Answer from: Vells962

We have that the measures of the angles are as follows

$\theta_1=80 \textdegree$

$\theta_2=75 \textdegree$

$\theta_3=25 \textdegree$

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

$\theta_1=Largest\ angle$

$\theta_2=Middle\ angle$

$\theta_3=Smallest\ angle$

Therefore

$\theta_1=55 \textdegree+\theta_3\\\\\theta_2=3*\theta_3$

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

$\theta_1+\theta_2+\theta_3=180$

Therefore

$55 \textdegree+\theta_3+3*\theta_3+\theta_3=180$

$\theta_3=25 \textdegree$

Therefore

Substitute $\theta_3$ into equations of $\theta_1$ and $\theta_2$

For $\theta_1$

$\theta_1=55 \textdegree+25 \textdegree\\\\\theta_1=80 \textdegree$

For $\theta_2$

$\theta_2=3*\theta_3$

$\theta_2=3*25 \textdegree$

$\theta_2=75 \textdegree$

in conclusion

The measures of the angles are as follows

$\theta_1=80 \textdegree$

$\theta_2=75 \textdegree$

$\theta_3=25 \textdegree$

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Answer from: jenn8055

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° .

Answer from: Quest

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

Answer from: Quest

The answer is option c.

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