Question

Pls Help

Answer 1

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 = $30^{\circ}$

Answer 2

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°