Question

1. given that ∠klm is a straight angle, find m∠kln and m∠nlm.

diagram: k---l---m (straight line), with point n forming angles (10x − 5)° and (4x + 3)° at l
m∠kln = \square °, m∠nlm = \square °

Explanation:

Step1: Set up the equation for a straight angle

A straight angle is \(180^\circ\), so the sum of \(m\angle KLN\) and \(m\angle NLM\) is \(180^\circ\). Thus, \((10x - 5)+(4x + 3)=180\).

Step2: Solve for \(x\)

Combine like terms: \(10x+4x - 5 + 3 = 180\) → \(14x - 2 = 180\).
Add 2 to both sides: \(14x = 182\).
Divide by 14: \(x=\frac{182}{14}=13\).

Step3: Find \(m\angle KLN\)

Substitute \(x = 13\) into \(10x - 5\): \(10(13)-5 = 130 - 5 = 125\).

Step4: Find \(m\angle NLM\)

Substitute \(x = 13\) into \(4x + 3\): \(4(13)+3 = 52 + 3 = 55\).

Answer:

\(m\angle KLN = \boldsymbol{125}^\circ\), \(m\angle NLM = \boldsymbol{55}^\circ\)