Question

In a quadrilateral ABCD. AB || CD ZA ZD = 4.5 and B2C = 2:3. Find
the measure of each angle of the quadrilateral
​

Answer 1

Answer:

∠A:∠D=2:3

Let ∠A and ∠D be 2x and 3x.

⇒  ∠B:∠C=7:8

Let ∠A and ∠D be 7y and 8y.

Since, AB∥CD and AD is a transversal.

∴  ∠A+∠D=180  

.           [ Interior angles on same side of transversal ]

⇒  2x+3x=180  

.

⇒  5x=180  

o

⇒  x=36  

⇒  ∠A=2×36  

=72  

⇒  ∠D=3×36  

=108  

.

Since, AB∥CD and BC is a transversal.

∴  ∠B+∠C=180   [ Interior angles on same side of transversal ]

⇒  7y+8y=180  

⇒  15y=180

∴  y=12  

⇒  ∠B=7×12  

=84  

⇒  ∠C=8×12  

=96  

Step-by-step explanation:

mark me as brainlist