Question

1. image of an angle with two adjacent angles labeled 2x + 10 and 4x + 20, forming a linear pair solve for x

a) 20 b)25 c)120 d)180

Explanation:

Step1: Identify angle relationship

The two angles form a linear pair, so their sum is \(180^\circ\). Thus, \((2x + 10)+(4x + 20)=180\).

Step2: Combine like terms

Simplify the left side: \(2x + 4x + 10 + 20 = 180\) → \(6x + 30 = 180\).

Step3: Solve for x

Subtract 30 from both sides: \(6x = 180 - 30\) → \(6x = 150\). Divide by 6: \(x=\frac{150}{6}=25\). Wait, no, wait—wait, let's recalculate. Wait, \(2x + 10 + 4x + 20 = 6x + 30\). Set equal to 180: \(6x = 150\)? Wait, no, 180 - 30 is 150? Wait, no, 180 - 30 is 150? Wait, 6x = 150? Then x = 25? But wait, let's check again. Wait, maybe I made a mistake. Wait, the angles: \(2x +10\) and \(4x +20\) are adjacent and form a straight line, so sum to 180. So:

\(2x + 10 + 4x + 20 = 180\)

Combine like terms: \(6x + 30 = 180\)

Subtract 30: \(6x = 150\)

Divide by 6: \(x = 25\)? Wait, but let's check the options. Option b is 25. Wait, but let's verify. If x=25, then 2x+10=60, 4x+20=120, 60+120=180. Yes, that works. Wait, but earlier I thought maybe a miscalculation, but no, that's correct. Wait, but wait, the problem's options: a)20, b)25, c)120, d)180. So when x=25, it works. So the correct answer is b)25. Wait, but let's do the steps again carefully.

Step1: Linear pair sum to 180

\((2x + 10) + (4x + 20) = 180\)

Step2: Combine like terms

\(2x + 4x + 10 + 20 = 180\)
\(6x + 30 = 180\)

Step3: Subtract 30 from both sides

\(6x = 180 - 30\)
\(6x = 150\)

Step4: Divide by 6

\(x = \frac{150}{6} = 25\)

Answer:

b)25