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If the measure of an angle is p is three times less than twice the measure of angle q and angle p and angle q are supplementary angles, find each angle measure

Respuesta :

lublana

Answer:

p=[tex]119^{\circ}[/tex] and q=[tex]61^{\circ}[/tex]

Step-by-step explanation:

We are given that  measure of an angle is P is three less than twice the measure of angle q.

We have to find the value of each angle

According to question

[tex]p+q=180^{\circ}[/tex] ( By definition of supplementary

[tex]p=2q-3[/tex]

Substitute the value

Then ,we get

[tex]2q-3+q=180[/tex]

[tex]3q=180+3[/tex]

[tex] 3q=183[/tex]

[tex]q=\frac{183}{3}=61[/tex]

Substitute the value of q then, we get

[tex]p=2(61)-3=122-3=119[/tex]

Hence, p=[tex]119^{\circ}[/tex] and q=[tex]61^{\circ}[/tex]

Using the concept of supplementary angles, it is found that:

  • Angle q measures 108 degrees.
  • Angle p measures 72 degrees.

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  • If two angles are supplementary, the sum of their measures is 180º.
  • Angle p is 3 times less than twice angle q, so: [tex]p = \frac{2q}{3}[/tex]
  • They are supplementary, thus: [tex]p + q = 180 \rightarrow p = 180 - q[/tex]

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Replacing the second equation into the first:

[tex]p = \frac{2q}{3}[/tex]

[tex]180 - q = \frac{2q}{3}[/tex]

[tex]2q = 540 - 3q[/tex]

[tex]5x = 540[/tex]

[tex]q = \frac{540}{5}[/tex]

[tex]q = 108[/tex]

And for p:

[tex]p = 180 - q = 180 - 108 = 72[/tex]

Angle q measures 108 degrees.

Angle p measures 72 degrees.

A similar problem is given at https://brainly.com/question/22826236

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