Question

Pls Help

Find the measure of angle x in the figure below:

Two triangles are shown such that one triangle is inverted and share a common vertex. The lower triangle has two angles at the base marked as 75 degrees each. The angle at the vertex of the inverted triangle at the top is marked as x degrees.


15°
25°
30°
60°

Answer 1

First solve the triangle:
75° + 75° + x = 180°
150° + x = 180°
x = 180° - 150°
Therefore x = 30°
Then, use the geometrical property of vertically opposite angles.
Therefore. x° = 30°

Answer 2

Answer: $30^{\circ}$

Step-by-step explanation:

In the given picture , we have two triangles ( one on another ) ,such that one triangle is inverted and share a common vertex. .

Then , the third angles of the lower triangle must be x   [∵ Vertical angles are congruent.]

When we consider the lower triangle, we have

$x+75^{\circ}+75^{\circ}=180^{\circ}$     [ By Angle sum property ]

$\Rightarrow\ x+150^{\circ}=180^{\circ}\\\\\Rightarrow\ x=180^{\circ}-150^{\circ}=30^{\circ}$

Hence, the measure of angle marked as x = $30^{\circ}$