Answer:
see explanation
Step-by-step explanation:
a and 85 form a straight angle and are supplementary, thus
a + 85 = 180 ( subtract 85 from both sides )
a = 95
b and 85 are vertical angles and are congruent, thus
b = 85
c and 85 are corresponding angles and congruent, thus
c = 85
c and d are vertical angles and congruent, thus
d = 85
In conclusion
a = 95, b = 85, c = 85, d = 85
4. Let the numbers be x - 2, x, and x + 2, where x is an odd number.
2(x² - 4) - 4x = (x + 2)² + 21
2x² - 8 - 4x = x² + 4x + 4 + 21
2x² - 4x - 8 = x² + 4x + 25
x² - 8x - 33 = 0
(x - 11)(x + 3) = 0
x = 11, or -3
When x = 11, x - 2 = 9, x + 2 = 13
When x = -3, x - 2 = -5, x + 2 = -1
Explanation: You are on the right track. However, rather than having three unknown variables, try to reduce your working out to one unknown variable. Since you know they are consecutive odd numbers, you can simply let x be the middle term and the other two be + and - 2, provided x is an odd number.
That will reduce your variable issues, and helps as the first and third provide a difference of two squares, and this works out very nicely.
Q5: is essentially the same process. Let your variables be something in the form of one unknown variable, and you should be okay from there. Let me know if you're stuck.
