Question

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Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Let the unknown angle be \(x\). The sum of angles in a triangle is \(180^{\circ}\).
For the lower triangle, the vertical - angle of the angle in the upper triangle is \(180^{\circ}-(35^{\circ}+23^{\circ})\).

$$180^{\circ}-(35^{\circ}+23^{\circ})=180^{\circ}-58^{\circ}=122^{\circ}$$

The sum of angles in the upper triangle: \(x + 27^{\circ}+(180^{\circ}-122^{\circ})=180^{\circ}\)

Step2: Solve for \(x\)

First, simplify \(180^{\circ}-122^{\circ}=58^{\circ}\). Then the equation for the upper - triangle angles is \(x+27^{\circ}+58^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(27^{\circ}+58^{\circ})$$

$$x = 95^{\circ}$$

Answer:

\(95^{\circ}\)