Question

Given: ZADB = ZCBD ZABDZCDB m ZA= 3x + 15 mZC=8x-20 Find: x and m ZA A4 D B ​

Answer 1

Answer: x = 7 and m∠A = 36

Explanation:

Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB

This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C

⇒3x +15 = 8x - 20

⇒3x + 15 - 3x = 8x - 3x -20

⇒5x = 20 + 15

⇒x = 7

Now m∠A = (3X7) +15 = 36

Answer 2

x = 7 , ∠ A = 36°

Explanation:

since ∠ ADB ≅ ∠ CBD ( alternate angles )

and ∠ ABD ≅ ∠ CDB ( alternate angles )

then ABCD is a parallelogram

the opposite angles of a parallelogram are congruent , so

∠ C = ∠ A , that is

8x - 20 = 3x + 15 ( subtract 3x from both sides )

5x - 20 = 15 ( add 20 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°