Question

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

Answer 1

20°

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

m∠1 = 20°

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°