Answer
132 degrees
Step-by-step explanation:
Strategy: Find angle DEB and using that fact that DEB + DEF is 180 degrees to find angle DEF
The sum of the four angles of any quadrilateral is 360 degrees.
Since three angles are given, we can use that to find the fourth.
360-(147+93+72)=size of angle DEB. Solving, you get angle DEB is 48.
Also, knowing that segment BF is a straight line, it means that angle DEB + angle DEF is equal to a straight angle (180 degrees).
DEB+DEF=180
48+DEF=180
DEF=180-48=132 degrees.
Thus, angle DEF is equal to 132 degrees.
Cross multiply:-
9 * x = 2 * 8
x = (2 * 8) / 9 = 16/9 or 1 7/9 answer
By the Pythagorean Theorem, the length of x is
a^2 + b^2 = c^2 Pythagorean Theorem
6^2 + b^2 = 10^2 Substitute known variables
6^2 + b^2 - 10^2 = 0 Subtract 10^2 from each side
6^2 - 10^2 = b^2 Subtract b^2 from each side
√6^2-10^2 = √b^2 Take square root of each side
8 = b Simplify
So, the length of x is 8. I hope this helps!
