SOLUTION
For 1-5 items
REMEMBER
- the diagonals of a rectangle are equal.
- Opposite sides are equal
- All angles are equal
- The vertices of the rectangles are 90°
1. CR = AE » Diagonals are equal «
- CR is half the value of AE
- Hence , CR = 46/2in
2. AR = CE » Opposite sides are equal «
3. CR = AE » Diagonals are equal «
4. <ACE = is a right angle »Angles are 90° «
5. <TRE + <ART = 90°
- <TRE + 56° = 90°
- <TRE = 90°-56°
- <TRE = 34°
For 6-7 items
REMEMBER
- All sides are equal
- All diagonals are equal
6. EA = AS » All sided are equal «
- 3x-11 = x+3
- 3x-x = 3+11
- 2x = 14
- x = 7
7. ES = AY » All diagonals are equal «
- ES = 4(7)-6in
- ES = 28-6in
- ES = 22in
For 8-10 items
REMEMBER
- All sides are equal
- Opposite angles are equal
- Sum of the adjacent angles is 180°
8. First, We will solve for the value of y
- The angles formed by the diagonals are 90°. It follows that:
- 2y+10 = 90
- 2y = 90-10
- 2y = 80
- y = 40
Now , <2 and <3 are equal
- <3 = y+20
- <3 = 40+20
- <3 = 60°
9. The sum of adjacent angles are 180°
- <3+<2 + 2(<JEP)= 180
- 60+60 + 2(<JEP) = 180
- 120+2(<JEP) = 180
- 2(<JEP) = 180-120
- 2(<JEP) = 60
- <JEP = 30°
10. EH = HO » All sides are equal «
- 2x-3 = x+1
- 2x-x = 1+3
- x = 4
Substitute the value of x
if EH = 2(4)-3 = 8-3 = 5 , then all the sides are equal to 5 also.
ANSWER
- 46/2in
- 25in
- 49in
- 90°
- 34°
- 7
- 22in
- 60°
- 30°
- 5
