Question

1.5 triangles
score: 0/16 answered: 0/16
question 1
in a certain triangle, the measure of angle a is three times as big as the measure of angle c and the measure of angle b is 55 degrees bigger than the measure of angle c. what is the degree measure of angle b?

Explanation:

Step1: Set up variables

Let the measure of angle \( C=x\) degrees. Then angle \( A = 3x\) degrees and angle \( B=x + 55\) degrees.

Step2: Use the triangle - angle sum formula

Since the sum of the interior angles of a triangle is \(180^{\circ}\), we have the equation \(A + B+C=180\). Substitute the expressions for \(A\), \(B\), and \(C\): \(3x+(x + 55)+x=180\).

Step3: Simplify the equation

Combine like terms: \(3x+x+x+55 = 180\), which gives \(5x+55=180\).

Step4: Solve for \(x\)

Subtract 55 from both sides: \(5x=180 - 55=125\). Then divide both sides by 5: \(x=\frac{125}{5}=25\).

Step5: Find the measure of angle \(B\)

Since \(B=x + 55\) and \(x = 25\), then \(B=25+55\).

Answer:

\(80\)