Question

Help me on this work asap

Answer 1

x = 19°

Explanation:

The given problem presents a figure of two triangles with certain angles provided and requires the determination of the angle labeled as 'x'. To solve for 'x', we'll employ the principles of triangle angle sum, supplementary angles, and vertical angles.

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Using supplementary angles we can determine the angle in the top right of the top triangle. Recall that supplementary angles add up to 180°.

`\Longrightarrow \text{Top Right $\angle$}=180\textdegree-150\textdegree\\\\\\\\\therefore \text{Top Right $\angle$}=30\textdegree`

The interior sum of angles inside a triangle equals 180°. Use this to find the bottom angle of the top triangle.

`\Longrightarrow \text{Bottom $\angle$}=180 \textdegree- 30\textdegree-57\textdegree\\\\\\\\\therefore \text{Bottom $\angle$}=93 \textdegree`

The bottom angle of the top triangle and the top angle of the bottom triangle are vertical angles. Thus, their angle measures are the same.

Knowing that the interior sum of angles in a triangle equals 180°. We can find 'x'.

`\Longrightarrow x=180\textdegree-93 \textdegree-68 \textdegree\\\\\\\\\therefore \boxed{x=19 \textdegree}`

Thus, x = 19°.