Use the fact that the sum of the 3 angles in a triangle is 180 ∘ to answer this question.One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 15 ∘ more than that of the smallest angle. Find the measure of the each of the angles.The SMALLEST angle has a measure of ?The MIDDLE angle has a measure of ?The LARGEST angle has a measure of ?

Question

Use the fact that the sum of the 3 angles in a triangle is       180          ∘       to answer this question.One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is       15          ∘       more than that of the smallest angle. Find the measure of the each of the angles.The SMALLEST angle has a measure of ?The MIDDLE angle has a measure of ?The LARGEST angle has a measure of ?

Mira Spears · Accepted Answer

Step 1Let the three angles of triangle are      x          ∘        =  s  m  a  l  l        y          ∘        =  m  i  d  d  l  e        z          ∘        =  l  a  r  g  e  s  tBy the given information, it is implied that      z          ∘        =  3      x          ∘      and       y          ∘        =      15          ∘        +      x          ∘      The sum of all angles of triangle is       180          ∘      i.e.,       x          ∘        +      y          ∘        +      z          ∘        =      180          ∘        ⇒      x          ∘        +      15          ∘        +      x          ∘        +  3      x          ∘        =      180          ∘          ⇒  5      x          ∘        +      15          ∘        =      180          ∘          ⇒  5      x          ∘        =      165          ∘              x          ∘        =      33          ∘      Smallest angle   =      33          ∘      Step 2Middle angle   ⇒      y          ∘        =      15          ∘        +      x          ∘        =      15          ∘        +      33          ∘        =      48          ∘      Largest angle   ⇒      z          ∘        =  3      x          ∘        =  3  (      33          ∘        )  =      99          ∘

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