Question

a challenge to brainly solve this qestion​

Answer 1

Properties to be known:

• Alternate Angles between two parallel lines are equal.
• Angle Sum Property: The Sum of all interior angles of a triangle add up to 180 degrees.

Solution:

According to the question,

→ x : y :: 3 : 2

→ x/y = 3/2

→ x = 3y/2   ... ( 1 )

Consider the right angled triangle. Applying Angle Sum property, we get:

→ x + y + 90° = 180°

→ 3y/2 + y = 180° - 90°

→  1.5y + y = 90°

→ 2.5y = 90°

→ y = 90° / 2.5

→ y = 36°

Therefore x = 1.5 × 36° = 54°

Now consider the straight line CD. We know that Angle in a straight line is 180°. Therefore we can write it as:

→ p + y + z = 180°

→ p + 100° = 180°   [ y + z = 100° ]

→ p = 180° - 100°

→ p = 80°

Now Consider Angle P and Angle x + Angle  A. We can see that they are Alternate Angles. Applying the property of Alternate angles we get:

→ p = x + a

→ 80° = 54° + a

→ 80° - 54° = a

→ a = 26°

Therefore the value of Angle 'a' is 26°.

Answer 2

Answer:

a = 26

Step-by-step explanation:

x/y = 3/2

2x = 3y ...1

Now,

P + y + z = 180

P = 80 (y + z = 100)

so,

P = x + a

=> 80 = x + a ....2

and,

x + y + 90 = 180

x = 90 - y

2x = 180 - 2y (multiplying equ by 2)

3y + 2y = 180 (from 1)

y = 36

Therefore, x = 180 - (90 + 36 )

x = 180 - 126

x = 54

Putting value of x in equ 2

We have,

80 = 54 + a

26 = a (Ans)