Questions: Name an angle or angles in the diagram shown to the right described by the following. Note that L lies on both overrightarrow(AH) and overrightarrow(NR). adjacent and congruent to angle ALK

Name an angle or angles in the diagram shown to the right described by the following. Note that L lies on both overrightarrow(AH) and overrightarrow(NR). adjacent and congruent to angle ALK

Transcript text: Name an angle or angles in the diagram shown to the right described by the following. Note that L lies on both $\overrightarrow{\mathrm{AH}}$ and $\overrightarrow{\mathrm{NR}}$. adjacent and congruent to $\angle A L K$

Solution

Solution Steps

Step 1: Identify the given angle

The given angle is ∠ALK. It measures 60°.

Step 2: Define adjacent angles

Adjacent angles share a vertex and a side but do not overlap. ∠ALK shares vertex L and side $\overrightarrow{\mathrm{LK}}$ with ∠KLH, and shares vertex L and side $\overrightarrow{\mathrm{LA}}$ with ∠NLA.

Step 3: Identify congruent angles

Congruent angles have equal measures. We are looking for an angle adjacent to ∠ALK that also measures 60°. Since lines AH and NR intersect to form right angles at L, ∠KLH measures 90° - 60° = 30°. ∠NLA is adjacent to ∠ALK. Since ∠ALK, ∠KLH, and ∠HLA form a straight angle, and ∠HLA is a right angle, m∠NLA + m∠ALK = 90°. m∠NLA + 60° = 90°, so m∠NLA = 30°. ∠RLN is adjacent to ∠NLA, and since ∠RLK = 60° and ∠KLN = 90°, we find that m∠RLN = m∠RLK - m∠NLK= 60°. So m∠RLN = 60°, and it is adjacent to ∠ALK.

Final Answer

∠RLN

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >

Thank you for your feedback.

Copied!