Angle BAD measures (2a + 25)° while Angle BCD measures (3a - 15)°
a. What is the value of a?
b. What is m Angle BAD?
c. What is m Angle CBA?
Questions:
• How did you find the value?
• What property did you apply to solve for m Angle CBA?
Answers
a = 40 ∠BAD = 105° , ∠CBA = 75° in a parallelogram ABCD ∠BAD = (2a + 25)° & ∠BCD = (3a - 15)°
Step-by-step explanation:
Missing information :
ABCD is a parallelogram
opposite angles of parallelogram are equal
=> ∠BAD = ∠BCD
=> 2a + 25 = 3a - 15
=> a = 40
∠BAD = (2a + 25) = 2 * 40 + 25 = 105°
sum of adjacent angles of a parallelogram = 180°
=> ∠BDA + ∠CBA = 180°
=> 105° + ∠CBA = 180°
=> ∠CBA = 75°
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Answer:Property of a parallelogram with regards to its angles:
∠BAD and ∠BCD are opposite angles of parallelogram ABCD. As a condition of a parallelogram, its two pairs of opposite angles are congruent.
∠BAD ≅ ∠BCD
m∠BAD = 2a + 5
m ∠BCD = 3a - 15
Equate the expression:
2a + 25 = 3a - 15
3a - 2a = 25 + 15
a = 40
Find m∠BAD by substituting 40 to a:
m∠BAD = 2(40) + 25 = 105°
∠BAD and ∠CBA are consecutive angles. Consecutive angles of a parallelogram are supplementary. Therefore, the sum of their measures is 180°.
Find m∠CBA:
m∠CBA = 180° - m∠BAD
m∠CBA = 180° - 105°
m∠CBA = 75°
What is the value of a:
a = 40
What is m∠BAD?
m∠BAD = 105°
What is m∠CBA?
m∠CBA = 75°
How did you find the value of a?
By equating the expressions that represent the measures of ∠BAD and ∠BCD which are congruent.
What property did you apply to solve for m∠CBA?
The property of a parallelogram where its consecutive angles are supplementary.
explanation:
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