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The measure of the second angle is 15 degrees more than the measure of the first angle the measure of the third angle is 45 degrees more than the measure of the first angle tine the measures of the interior angles in the triangle

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cnate999

Answer:

The measures of the three interior angles of the triangle are {40,55,85}.

Step-by-step explanation:

Let a = the measure of the first angle of the triangle.

Let b = the measure of the second angle of the triangle.

Let c = the measure of the third angle of the triangle.

The problem statement tells us that

(1) a = a

(2) b = a + 15 and

(3) c = a + 45

Now we (should) know that the sum of the three angles of a triangle is 180 degrees. Then we get

(4) a + b + c = 180 or by substitution we get

(5) a + (a + 15) + (a + 45) = 180 or

(6) a + a + 15 + a + 45 = 180 or

(7) 3*a + 60 = 180 or

(8) 3*a = 180 - 60 or

(9) 3*a = 120

 

Now divide both sides of (9) by 3 to get

(10) 3*a/3 = 120/3 or

(11) a = 40

Using (2) and (3) we get

(12) b = 40 + 15 or

(13) b = 55 and

(14) c = 40 + 45 or

(15) c = 55

Always check the answer. Use (4)

Is (40 + 55 + 85 = 180)?

Is (95 + 85 = 180)?

Is (180 = 180)? Yes

The measures of the three interior angles would be as follows:

40°,55°,85°

If we assume the first angle(∠1) to be [tex]x[/tex],

so, the second angle(∠2) [tex]= x + 15[/tex]

while the third angle(∠3) [tex]= x + 45[/tex]

Through the Angle Sum Property, we know:

∠1 + ∠2 + ∠3 = 180°

By applying the above expressions, we get

[tex]x + (x + 15) + (x + 45) = 180[/tex]°

⇒ [tex]3x + 60 = 180[/tex]

⇒ [tex]3x = 180 - 60[/tex]

⇒ [tex]x = 120/3[/tex]

∵ [tex]x = 40[/tex]°

Therefore,

∠1 = 40°

∠2 = 40° + 15°

= 55°

∠3 = 40° + 45°

= 85°

Thus, the measures of the angles are 40°,55°, and 85°

Learn more about "Angles" here:

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