Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

If ABCD is a rectangle, and m_ADB = 55°, what is the value of x? A. 80 O B. 90 O C. 40 O D. 70 O E. 110​

If ABCD Is A Rectangle And MADB 55 What Is The Value Of X A 80 O B 90 O C 40 O D 70 O E 110 class=

Sagot :

Answer:  D) 70

===========================================================

Explanation:

Label a new point E at the intersection of the diagonals. The goal is to find angle CEB. Notice how angle AED and angle CEB are vertical angles, so angle AED is also x.

Recall that any rectangle has each diagonal that is the same length, and each diagonal cuts each other in half (aka bisect). This must mean segments DE and AE are the same length, and furthermore, triangle AED is isosceles.

Triangle AED being isosceles then tells us that the base angles ADE and DAE are the same measure (both being 55 in this case).

---------------------

To briefly summarize so far, we have these interior angles of triangle ADE

  • A = 55
  • D = 55
  • E = x

For any triangle, the three angles always add to 180, so,

A+D+E = 180

55+55+x = 180

110+x = 180

x = 180-110

x = 70

View image jimthompson5910
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.