Question

in the figure, m∠1 = (6x)° and m∠2 = (x + 26)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: (b) find the degree measure of each angle. m∠1 = ° m∠2 = °

Explanation:

Step1: Identify angle relationship

Angles 1 and 2 form a linear pair, so their sum is \(180^\circ\). Thus, \(6x + (x + 26) = 180\).

Step2: Solve for \(x\)

Combine like terms: \(7x + 26 = 180\). Subtract 26: \(7x = 154\). Divide by 7: \(x = 22\).

Step3: Find \(m\angle 1\)

Substitute \(x = 22\) into \(6x\): \(6(22) = 132\).

Step4: Find \(m\angle 2\)

Substitute \(x = 22\) into \(x + 26\): \(22 + 26 = 48\).

Answer:

(a) Equation: \(6x + x + 26 = 180\)
(b) \(m\angle 1 = 132^\circ\), \(m\angle 2 = 48^\circ\)