Given:
m∠APD = (7x + 1)°
m∠DPC = 90°
m∠CPB = (9x - 7)°
To find:
The measure of arc ACD.
Solution:
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠APD + m∠DPC + m∠CPB = 180°
7x° + 1° + 90° + 9x° - 7° = 180°
16x° + 84° = 180°
Subtract 84° from both sides.
16x° + 84° - 84° = 180° - 84°
16x° = 96°
Divide by 16° on both sides.
x = 6
m∠APB = 180°
m∠BPD = (9x - 7)° + 90°
= (9(6) - 7)° + 90°
= 47° + 90°
m∠BPD = 137°
m∠APD = m∠APB + m∠BPD
= 180° + 137°
= 317°
<em>The measure of the central angle is congruent to the measure of the intercepted arc.</em>
m(ar ACD) = m∠APD
m(ar ACD) = 317°
The arc measure of ACD is 317°.
The next step of your proof is to subtract (a/b) from both sides.
Then you get, x = (m/n) - (a/b)
Since rationals are closed over addition, (m/n) + (-a/b) is a rational number.
Therefore, x (an irrational number) = a rational number <em>This is a false statement which is a contradiction. So, the assumption was incorrect.</em>
Thus, the sum of a rational and irrational number is an irrational number. QED
Answer:
False.
Step-by-step explanation:
Because 12 and 9 are both multiples of 3.
Answer:
(B)permits only certain substances to leave but all to enter
