Answer:
b = 87°
Step-by-step explanation:
In order to answer this question, we need to utilise an important angle fact which is <em>angles in a quadrilateral add up to 360° </em>
Using the information we can set up an equation to find the value of b
→ Form equation
63 + 140 + 70 + b = 360
→ Simplify
273 + b = 360
→ Minus 273 from both sides isolate b
b = 87°
Answer:
d = 233.23 feet
Step-by-step explanation:
Given that,
Justin walks 200 feet to the east, then turns and walks 120 feet due south.
We need to find the total distance walked by Justin. Let the distance be d.
We can use the Pythagoras theorem to find it such that,

So, he walk 233.23 feet in all.
Answer:
170
Step-by-step explanation:
Answer: 14
The number to the right of the decimal point is either 5 or greater than that, so the 13 is increased by 1 which results in 14.
Answer:
Area of trapezium = 4.4132 R²
Step-by-step explanation:
Given, MNPK is a trapezoid
MN = PK and ∠NMK = 65°
OT = R.
⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).
Now, sum of interior angles in a quadrilateral of 4 sides = 360°.
⇒ x + x + 65° + 65° = 360°
⇒ x = 115°.
Here, NS is a tangent to the circle and ∠NSO = 90°
consider triangle NOS;
line joining O and N bisects the angle ∠MNP
⇒ ∠ONS =
= 57.5°
Now, tan(57.5°) = 
⇒ 1.5697 = 
⇒ SN = 0.637 R
⇒ NP = 2×SN = 2× 0.637 R = 1.274 R
Now, draw a line parallel to ST from N to line MK
let the intersection point be Q.
⇒ NQ = 2R
Consider triangle NQM,
tan(∠NMQ) = 
⇒ tan65° =
⇒ QM =
QM = 0.9326 R .
⇒ MT = MQ + QT
= 0.9326 R + 0.637 R (as QT = SN)
⇒ MT = 1.5696 R
⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R
Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).
⇒ A = (
) × (ST)
= (
) × 2 R
= 4.4132 R²
⇒ Area of trapezium = 4.4132 R²