(05.02)find the measure of angle x in the figure below: two triangles are shown such that one triangle is inverted and they share a common vertex. the lower triangle has two angles at the base. the lower left angle is marked as 55 degrees. the lower right angle is marked as 30 degrees. the angle at the vertex of the inverted triangle at the top is marked as x degrees.

Step-by-step explanation:

We are given that: Two triangles are such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 55 degrees. The lower right angle is marked as 30 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees.

The figure of such a triangle is attached to the answer.

As we know that sum of all the angles of a triangle is equal to 180°.

⇒ 55°+30°+x=180°

⇒  85°+x=180°

⇒ x=180°-85°

⇒ x=95°

Hence, the angle at the vertex is 95°.

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