Question

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

Answer 1

∠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`