How to find the missing measurements ?
1 answer:
Answer:
CD = 10
AD = 22
EC = 13
AC = 26
∠CAD = 23°
∠BAC = 47°
∠ADC =110°
Step-by-step explanation:
A parallelogram is a quadrilateral with two sets of opposite parallel lines.
Which mean in ABCD parallelogram given AB is parallel to DC and BC is parallel to AD.
Now lets find the values required,
CD = AB (Opposite sides are equal in length)
But, AB= 10 (given) therefore CD = 10.
AD = BC (Opposite sides are equal in length)
But, BC= 22 (given) therefore AD = 22.
EC = AE (Diagonals bisect each other)
But, AE= 13 (given) therefore EC = 13
AC = AE + EC
=
AC =
∠CAD = ∠BCA (Alternate interior angles are equal)
But, ∠BCA = 23° therefore, ∠CAD = 23°
∠BAC = ∠ACD (Alternate interior angles are equal)
But, ∠ACD = 47° therefore, ∠BAC = 47°
∠ADC + ∠BCD = 180° (Consecutive interior angles)
But, ∠BCD = 23°+47°=70°
∠ADC = 180°- ∠BCD
=180°-70°
∠ADC =110°
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<h3>Answer: Choice A, 29 degrees</h3>
Central angle CBA is a right angle, so it is 90 degrees. This means the arc measure from A to C, following the shortest path on the curve, is 90 degrees. This is minor arc CA. A minor arc is one that is less than 180 degrees in measure.
We want to find the measure of minor arc DE. This is the last piece of the puzzle, so to speak, that forms the entire arc ACD. This arc is 180 degrees because AD is a diameter.
So,
(minor arc DE) + (minor arc EC) + (minor arc CA) = arc ACD
x + 61 + 90 = 180
x + 151 = 180
x + 151 - 151 = 180 - 151 .... subtract 151 from both sides
x = 29
Minor arc DE is 29 degrees.
Check out the attached image below if you're still stuck. Hopefully the image clears any confusion you may have.