Question

If the angles of a quadrilateral are 4x, 3x + 10°, 2x + 10º and 4x + 15°, then find the
angles.​

Answer 1

$4x + 3x + 10 +2x + 10 + 4x + 15 = 360 \\ 13x + 35 = 360 \\ 13x = 360 -35 = 325 \\ x= \frac{325}{13} = 25 \\ \\ 4x = 4 \times 25 = 100 \\ 3x + 10 = 3 \times 25 +10 = 85 \\ 2x + 10 = 2 \times 25 + 10 = 60 \\ 4x + 15 = 4 \times 25 + 15 = 115$

Answer 2

Answer:

Angles of a quadrilateral are 100°, 85°, 60° and 115° respectively.

Step-by-step explanation:

Let us suppose that ABCD is a quadrilateral.

Given that:

Angles of quadrilateral ABCD are:→

• ∠A = 4x
• ∠B = 3x + 10°
• ∠C = 2x + 10°
• ∠D = 4x + 15°

We know that:

Sum of all the four angles of a quadrilateral is equal to 360°.

i.e., ∠A + ∠B + ∠C + ∠D = 360°

According to the question:

→ 4x + 3x + 10° + 2x + 10º + 4x + 15° = 360°

→ 4x + 3x + 2x + 4x + 10° + 10° + 15° = 360°

→ 13x + 35° = 360°

→ 13x = 360° - 35°

→ 13x = 325°

→ x = 325°/13

→ x = 25°

∴ Angles of quadrilateral ABCD are:

• ∠A = 4x = 4 × 25° = 100°
• ∠B = 3x + 10° = 3 × 25° + 10° = 75° + 10° = 85°
• ∠C = 2x + 10° = 2 × 25° + 10° = 50° + 10° = 60°
• ∠D = 4x + 15° = 4 × 25° + 15° = 100° + 15° = 115°