Question

which angle pair is adjacent and complementary?
\\( \angle m l k \\) and \\( \angle k l j \\)
\\( \angle g l h \\) and \\( \angle g l m \\)
\\( \angle m l j \\) and \\( \angle a e b \\)
\\( \angle c e b \\) and \\( \angle b e a \\)

Explanation:

Step1: Recall the definitions of adjacent and complementary angles

Adjacent angles: Angles that have a common vertex and a common side. Complementary angles: Two angles whose sum is \(90^{\circ}\).

Step2: Analyze \(\angle MLK\) and \(\angle KLJ\)

• Common vertex and side: Both angles have vertex \(L\) and common side \(LK\), so they are adjacent.
• Sum of angles: \(\angle MLK+\angle KLJ = 60^{\circ}+ 30^{\circ}=90^{\circ}\), so they are complementary.

Step3: Analyze \(\angle GLH\) and \(\angle GLM\)

• Common vertex and side: They have vertex \(L\) and common side \(LG\), so they are adjacent.
• Sum of angles: \(\angle GLH+\angle GLM=60^{\circ}+(180 - 60 - 30)^{\circ}=60^{\circ}+90^{\circ}=150^{\circ}

eq90^{\circ}\), so they are not complementary.

Step4: Analyze \(\angle MLJ\) and \(\angle AEB\)

• Common vertex and side: \(\angle MLJ\) has vertex \(L\), \(\angle AEB\) has vertex \(E\). They do not have a common vertex and side, so they are not adjacent.

Step5: Analyze \(\angle CEB\) and \(\angle BEA\)

• Common vertex and side: They have vertex \(E\) and common side \(BE\), so they are adjacent.
• Sum of angles: \(\angle CEB+\angle BEA = 180^{\circ}\) (they form a linear - pair), so they are supplementary, not complementary.

Answer:

\(\angle MLK\) and \(\angle KLJ\)