Question

question 6
the angles of a triangle add up to 180 degrees.
the second angle is 15 degrees larger than the smallest angle.
the third angle is 3 times as big as the smallest angle.
find the measure of the smallest angle (in degrees)

Explanation:

Step1: Let the smallest angle be $x$.

Let the smallest angle be $x$ degrees. Then the second - angle is $x + 15$ degrees and the third - angle is $3x$ degrees.

Step2: Set up an equation based on the angle - sum property of a triangle.

Since the sum of the angles of a triangle is 180 degrees, we have the equation $x+(x + 15)+3x=180$.

Step3: Combine like terms.

Combining like terms on the left - hand side gives $5x+15 = 180$.

Step4: Isolate the variable term.

Subtract 15 from both sides of the equation: $5x=180 - 15$, so $5x=165$.

Step5: Solve for $x$.

Divide both sides of the equation by 5: $x=\frac{165}{5}=33$.

Answer:

33