Question

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Answer 1

Answer:

1) $m\angle x = 35^{\circ}$, 2) $m\angle x = 60^{\circ}$, 3) $m \angle x = 40^{\circ}$

Step-by-step explanation:

1) Triangle is a right triangle since tangent line is perpendicular to the radius of the circle. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$:

$m\angle x = 180^{\circ} - 90^{\circ} - 55^{\circ}$

$m\angle x = 35^{\circ}$

2) Both triangles are symmetrical right triangles since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$:

$m \angle x = 180^{\circ} - 90^{\circ} - 30^{\circ}$

$m\angle x = 60^{\circ}$

3) The figure is formed by two symmetrical right triangles. These triangles are right-angled and symmetrical since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in quadrilaterals equals 360°, we find the value of the angle $x$:

$m\angle x = 360^{\circ} - 180^{\circ} - 140^{\circ}$

$m \angle x = 40^{\circ}$