Hello There!
Here is your answer!
Question:
The angles of a quadrilateral have measures of 5x, 3x + 20, 4x + 5, and 5x -5. The measure of one of the angles is ?
solution:
The measures of each of the angles are 100°,80°,85° and 95° respectively...
Step-by-step Explanation:-
• As we know, Sum of all the angles of the quadrilateral measures 360° ..
- So, we have to add the given angles to find the measures of each one...
→ 5x + ( 3x+ 20 ) + ( 4x + 5 ) + ( 5x - 5 ) = 360
→ 5x + 3x + 20 + 4x + 5 + 5x - 5 = 360
Taking like terms,
→ 5x + 3x + 4x + 5x + 20 + 5 - 5 = 360
→ 17x + 20 = 360
→ 17x = 360 - 20
→ 17x = 340
→ x = 340 / 17
→ x = 20
Now putting the values into places,
Angle 1 :- 5x = 5(20) = 100°
Angle 2 :- (3x+20) = 3(20) + 20 = 60 + 20 = 80°
Angle 3 :- (4x+5) = 4(20) + 5 = 80 + 5 = 85°
Angle 4 :- (5x-5) = 5(20) - 5 = 100 - 5 = 95°
Hence, The measure of each of the angles are 100° , 80° , 85° and 95° respectively...
Hope this helps you ◉‿◉
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