Question

In the adjoining figure, the parallel lines are marked by arrow lines. The value of angle 1 is:

Answer 1

Answer:

20°

Step-by-step explanation:

40°, 70° and 90° are the measures of the three angles of the quadrilateral.

Measure of fourth angle of the Quadrilateral

= 360° - (40° + 70° + 90°)

= 360° - 200°

= 160°

Measure of angle 1 will be equal to the measure of the linear pair angle of 160° as they are corresponding angles.

Thus,

$m\angle 1 = 180\degree- 160\degree$

$\implies\huge\purple{\boxed{ m\angle 1 = 20\degree}}$

Alternate method:

$m\angle 1 = 180\degree- [360\degree-(40\degree+70\degree+90\degree)]$

$\implies m\angle 1 = 180\degree- [360\degree-200\degree]$

$\implies m\angle 1 = 180\degree- 160\degree$

$\implies m\angle 1 = 20\degree$

Answer 2

Answer:

m∠1 = 20°

Step-by-step explanation:

Alternate interior angle theorem (z-angles): when two parallel lines are cut by a transversal, the resulting alternate interior angles are equal.

Therefore, because of the parallel lines, angle 1 is equal to the missing angle in the quadrilateral (see attached diagram - alternate angles marked in red).

Let x = unknown angle in the quadrilateral (marked in blue on attached diagram)

Sum of interior angles of a quadrilateral = 360°

⇒ x + 40° + 70° + 90° = 360°

⇒ x + 200° = 360°

⇒ x = 160°

Angles on a straight line add up to 180°

⇒ x + m∠1 = 180°

⇒ 160° + m∠1 = 180°

⇒ m∠1 = 20°