Question

question 5 of 10
what is the value of y?
a. 85°
b. 10°
c. 110°
d. 55°

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(40^{\circ}+y^{\circ}+(y + 30)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(40 + y+y + 30=180\), which simplifies to \(2y+70 = 180\).

Step3: Solve for \(y\)

Subtract 70 from both sides: \(2y=180 - 70\), so \(2y=110\). Then divide both sides by 2: \(y=\frac{110}{2}=55\).

Answer:

D. \(55^{\circ}\)