Answer:
1. ∠LOQ = 80°
2. ∠LRQ = 40°
3. ∠LBQ = 40°
Step-by-step explanation:
- The measure of a central angle (angle that goes to the center of the circle) is EQUAL to the ARC from which it is intercepted.
- The measure of the angle that is on opposite side, on the circumference, of the circle is HALF of the ARC from which it is intercepted.
It is given that ARC QL has a measure of 80.
- Central angle from ARC QL (with same measure) are angle LOQ only.
- Opposite angles (half of measure of ARC QL) from ARC QL (on opposite side on circumference) are angles LRQ and LBQ.
<u>1.</u>
m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.
∠LOQ = 80°
<u>2.</u>
m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.
∠LRQ =
∠LRQ = 40°
<u>3.</u>
m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.
∠LBQ =
∠LBQ = 40°
Answer:
m<Q = 133°
Step-by-step explanation:
From the question given above, the following data were obtained:
m<P = (x + 13)°
m<Q = (10x + 13)°
m<R = (2x – 2)°
m<Q =?
Next, we shall determine the value of x. This can be obtained as follow:
m<P + m<Q + m<R = 180 (sum of angles in a triangle)
(x + 13)° + (10x + 13)° + (2x – 2)° = 180
x + 13 + 10x + 13 + 2x – 2 = 180
x + 10x + 2x + 13 + 13 – 2 = 180
13x + 24 = 180
Collect like terms
13x = 180 – 24
13x = 156
Divide both side by 13
x = 156 / 13
x = 12
Finally, we shall determine m<Q. This can be obtained as follow:
m<Q = (10x + 13)°
x = 12
m<Q = 10(12) + 13
m<Q = 120 + 13
m<Q = 133°
Check the attached answer.
Given that total volume of the solution = 12 quarts
Let volume of water added = x quarts
Then volume of 30% vinegar = (12-x) quarts
Given that x quarts of 0% water is mixed with (12-x)quarts of 30% vinegar to obtain 12 quarts of 25% solution
So we can write equation as:
[0% of x] + [30% of (12-x)] = [25% of 12]
or 0x + 0.30(12-x) = 0.25*12
or 0 + 3.6-0.30x = 3
or -0.30x = 3-3.6
or -0.30x = -0.6
x=2
Hence answer will be 2 quarts of water.
Answer: First step would be to do whatever is inside the parentheses.
Step-by-step explanation:
PEMDAS