Question

for the value of b. (2b+4)° (3b+1)° your answer b = 1.2

Explanation:

Step1: Identify angle relationship

The two angles \((2b + 4)^\circ\) and \((3b + 1)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[
(2b + 4)+(3b + 1)=180
\]

Step2: Combine like terms

Combine the \(b\) terms and the constant terms:
\[
2b+3b + 4 + 1=180\\
5b+5 = 180
\]

Step3: Solve for \(b\)

Subtract 5 from both sides:
\[
5b=180 - 5\\
5b=175
\]
Divide both sides by 5:
\[
b=\frac{175}{5}\\
b = 35
\]
Wait, there was a mistake in the initial answer. Let's re - check. Wait, maybe the angles are complementary? No, the diagram shows a linear pair (they are adjacent and form a straight line), so they should be supplementary. Wait, maybe I misread the angles. Wait, if the angles are \((2b + 4)\) and \((3b+1)\) and they are supplementary:

Wait, let's do it again.

Step1: Set up the equation

Since the two angles form a linear pair, their sum is \(180^\circ\). So:
\[
(2b + 4)+(3b + 1)=180
\]

Step2: Simplify the left - hand side

\[
2b+3b+4 + 1=180\\
5b + 5=180
\]

Step3: Subtract 5 from both sides

\[
5b=180 - 5\\
5b=175
\]

Step4: Divide both sides by 5

\[
b=\frac{175}{5}\\
b = 35
\]

The initial answer of \(b = 1.2\) is incorrect. The correct value of \(b\) is obtained by recognizing that the two angles are supplementary (sum to \(180^\circ\)) and then solving the resulting linear equation.

Answer:

\(b = 35\)