Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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

In The Adjoining Figure The Parallel Lines Are Marked By Arrow Lines The Value Of Angle 1 Is class=

Sagot :

Hrishii

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,

[tex]m\angle 1 = 180\degree- 160\degree[/tex]

[tex]\implies\huge\purple{\boxed{ m\angle 1 = 20\degree}}[/tex]

Alternate method:

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

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

[tex]\implies m\angle 1 = 180\degree- 160\degree[/tex]

[tex]\implies m\angle 1 = 20\degree[/tex]

semsee45

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°

View image semsee45
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.