Question

the diagram shows a triangle. the angles of the triangle are ( y + 44^circ ), ( 2y + 14^circ ), and ( y + 38^circ ). what is the value of ( y )? ( y = \boxed{}^circ ) submit.

Explanation:

Step1: Sum of triangle angles is \(180^\circ\)

The three angles are \(y + 44^\circ\), \(2y + 14^\circ\), and \(y + 38^\circ\). So, \((y + 44) + (2y + 14) + (y + 38) = 180\).

Step2: Combine like terms

Simplify the left - hand side: \(y+2y + y+44 + 14+38=4y + 96\). So the equation becomes \(4y+96 = 180\).

Step3: Solve for \(y\)

Subtract 96 from both sides: \(4y=180 - 96=84\). Then divide both sides by 4: \(y=\frac{84}{4} = 21\).

Answer:

\(21\)