Question

use the diagram below. if angle 2 equals (2x + 5)° and angle 3 equals 85°, what is the value of x? a. 35 b. 40 c. 45 d. 50

Explanation:

Step1: Identify angle - relationship

Angles 2 and 3 are supplementary (linear - pair), so $\angle2+\angle3 = 180^{\circ}$.

Step2: Substitute angle values

Substitute $\angle2=(2x + 5)^{\circ}$ and $\angle3 = 85^{\circ}$ into the equation: $(2x+5)+85=180$.

Step3: Simplify the equation

Combine like - terms: $2x+(5 + 85)=180$, which gives $2x+90 = 180$.

Step4: Solve for x

Subtract 90 from both sides: $2x=180 - 90$, so $2x=90$. Then divide both sides by 2: $x=\frac{90}{2}=45$.

Answer:

C. 45