Question

If the angles of a quadrilateral are ( 2x + 9 ) . ( x - 2 ) . ( 3x + 8 ) and ( 4x + 5 ) What is the measure of largest interior angle of the quadrilateral ?​

Answer 1

Solution:

Given –

• The angles of a quadrilateral are - (2x + 9)°, (x - 2)°, (3x + 8)°, (4x + 5)°.

We have to find out the largest interior angle of the quadrilateral.

We know that -

→ Sum of interior angles of a quadrilateral is 360°.

So, according to the given condition,

→ (2x + 9)° + (x - 2)° + (3x + 8)° +(4x + 5)° = 360°

→ 10x + 20° = 360°

→ 10x = 340°

→ x = 34°

Now, the angles are -

→ (2x + 9)° = 2 × 34 + 9 = 68° + 9° = 77°

→ (x - 2)° = 32°

→ (3x + 8)° = 3 × 34 + 8° = 102° + 8° = 110°

→ (4x + 5)° = 4 × 34 + 5° = 136° + 5° = 141°

• So, the value of the largest interior angle is 141°.

Answer:

• The value of the largest interior angle is 141°.