2 Answers

Isanka Thalagala · Answer 1 · 2021-04-02T23:32:51+0000

x =30°

Explanation:

Step 1: To find
$\angle \mathrm{KNL}$ .

Given N ∈ KO, where KO is a line.

Sum of the adjacent angles in a straight line is 180°.

$\Rightarrow \angle \mathrm{KNL}+\angle \mathrm{LNM}+\angle \mathrm{MNO}=180^(\circ)$

$\Rightarrow \angle \mathrm{KNL}+45^(\circ)+105^(\circ)=180^(\circ)$

$\Rightarrow \angle \mathrm{KNL}+150^(\circ)=180^(\circ)$

$\Rightarrow \angle \mathrm{KNL}=180^(\circ)-150^(\circ)$

$\Rightarrow \angle \mathrm{KNL}=30^(\circ)$

Step 2: To find
$\angle \mathrm{NLK}$ .

Sum of the adjacent angles in a straight line is 180°.

Given
$\angle \mathrm{NLM}=90^(\circ)$

$\Rightarrow \angle \mathrm{NLM}+\angle \mathrm{NLK}=180^(\circ)$

$\Rightarrow \angle \mathrm{NLK}=180^(\circ)-90^(\circ)$

$\Rightarrow \angle \mathrm{NLK}=90^(\circ)$

Step 3: To find x.

Sum of the interior angles in a triangle is 180°.

Let us take the triangle NLK.

$\Rightarrow \angle \mathrm{KNL}+\angle \mathrm{NLK}+\angle \mathrm{LKN}=180^(\circ)$

⇒ 30° + 90° + 2x = 180°

⇒ 2x = 180° – 30° – 90°

⇒ 2x = 60°

⇒ x = 30°

Hence, x = 30°.

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