Answer:
<A must be congruent to <A, <P must be congruent to <P, <Q must be congruent to <S, and <R must be congruent to <R
Step-by-step explanation:
Answer:
approximately 11 years
Step-by-step explanation:
Use the compound interest formula:
A = P(1+r)^n, where r is the annual interest rate as a decimal fraction and t is the number of years.
Here we have:
(10000 pounds) = (6500 pounds)(1 + 0.04)^t and must find the value of t.
Solve for (1.04)^t by dividing both sides of this equation by (6500 pounds):
1.5385 = 1.04^t
Take the log of both sides:
log 1.5385 = t*log 1.04, or
log 1.5385
t = -------------------- = (0.1871)/0.0170 = 10.98, or approximately 11 years
log 1.04
Using the same-side interior angles theorem, the values of x and y are:
x = 80
y = 130
<h3>What is the Same-side Interior Angles Theorem?</h3>
The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.
(x - 30) and (x + 50) are same-side interior angles, therefore:
(x - 30) + (x + 50) = 180
Solve for x
x - 30 + x + 50 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80
(x - 30) + y = 180
Plug in the value of x
(80 - 30) + y = 180
50 + y = 180
y = 180 - 50
y = 130
Learn more about the same-side interior angles theorem on:
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Answer:
Post questions with content only :)
Answer:
The answer is below
Step-by-step explanation:
Two polygons are said to be congruent if they have the same size and shape that is their corresponding angles and sides are equal.
Hence since Quadrilaterals ABCD is congruent to EFGH, then their corresponding angles and sides are equal.
In quadrilateral ABCD:
∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)
Substituting:
47 + 39 + 112 + ∠D = 360
∠D + 198 = 360
∠D = 360 - 198
∠D = 162°
The image of Quadrilaterals ABCD and EFGH is not given but let us assume that they have the same orientation, hence:
∠A = ∠E = 47°
∠B = ∠F = 39°
∠C = ∠G = 112°
∠D = ∠H = 162°
