Question

1. y= x= 3x° (2x + 13)° 57° y°

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(y = 3x+57\). Also, the sum of angles in a triangle is \(180^{\circ}\). So, \(3x+(2x + 13)+57=180\).

Step2: Solve the equation for \(x\)

Simplify the equation \(3x+(2x + 13)+57=180\).
First, combine like terms: \(3x+2x+13 + 57=180\), which gives \(5x+70 = 180\).
Subtract 70 from both sides: \(5x=180 - 70\), so \(5x=110\).
Divide both sides by 5: \(x=\frac{110}{5}=22\).

Step3: Find the value of \(y\)

Substitute \(x = 22\) into \(y = 3x+57\).
\(y=3\times22+57\).
First, calculate \(3\times22 = 66\). Then \(y=66 + 57=123\).

Answer:

\(y = 123\), \(x = 22\)