only do question 14diagrams are not drawn to scale. i only care about the answers & the steps you did to get the answers.don’t be slow pls (:

Question

asked Aug 22, 2023 183k views

1 Answer

Serhii · Answer 1 · 2023-08-28T08:25:41+0000

∠KU and ∠LE are vertically opposite angles, which means that they are congruent, so that:

$\angle KU=\angle LE=60º$

∠LUE and ∠LKE intersect the same arc mLE, which means that they are congruent:

$\angle\text{LUE}=\angle\text{LKE}=32º$

∠KU and the vertex angle marked in blue are supplementary angles, which means that they add up to 180º:

$\begin{gathered} 60+x=180º \\ x=180-60 \\ x=120º \end{gathered}$

Knowing two of the three angles of the upper triangle, you can calculate the measure of the missing one, ∠ULK:

$\begin{gathered} 32+120+\angle\text{ULK}=180 \\ 152+\angle\text{ULK}=180 \\ \angle\text{ULK}=180-152 \\ \angle\text{ULK}=28º \end{gathered}$

∠ULK and ∠UEK intercept the same arc mKU, so they are congruent:

$\angle\text{ULK}=\angle\text{UEK}=28º$