Question

the sum of two angles of a quadrilateral is 150 and the other angles are in the ratio 2:3 find the measure of each angle
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Answer 1

Given :-

1. Sum of 2 angles of a quadrilateral is 150°
2. Other 2 angles are in the ratio 2:3

To find :-

• Measure of each angle = ?

Solution :-

Let the 4 angles of a quadrilateral be ∠A, ∠B, ∠C and ∠D

According to the question,

★ ∠A + ∠B = 150°

∠A + ∠B = 150°★ ∠C = 2x

∠A + ∠B = 150°★ ∠C = 2x★ ∠D = 3x

Concept used :-

• Sum of all angles in any quadrilateral is 360°

Method :-

∠A + ∠B + ∠C + ∠D = 360°

→ (∠A + ∠B) + ∠C + ∠D = 360°

→ 150° + 2x + 3x = 360°

→ 150 + 5x = 360°

→ 5x = 360 - 150

→ 5x = 210°

→ x = 42°

For finding the angles,

∠C = 2x = 2(42) = 84°

∠D = 3x = 3(42) = 126°

∴ The measure of 2 angles are 84° and 126°

Answer 2

Given :-

• Sum of two angles of a quadrilateral is 150°
• Ratio of other angles is 2 : 3

To Find :-

• Measure of each angle of that quadrilateral

Solution :-

❒ Let the quadrilateral be ( ABCD ) , then ATQ ::

   ★ ∠A + ∠B = 150° ★

   ★ ∠C : ∠D = 2 : 3 ★

~Here , measure of angle ∠C is 2x° and ∠D is 3x°

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

$\sf \bigstar$ Sum of all angles of a quadrilateral is 360°

➼ Finding value of x ::

$\sf \mapsto$ ∠A + ∠B + ∠C + ∠D = 360°

( given ∠A + ∠B = 150 )

$\sf \mapsto$ 150° + ∠C + ∠D = 360°

( ∠C = 2x° and ∠D = 3x° )

$\sf \mapsto$ 150° + 2x° + 3x° = 360°

$\sf \mapsto$ 150° + 5x° = 360°

$\sf \mapsto$ 5x = 360° - 150°

$\sf \mapsto$ 5x = 210°

$\sf \mapsto x = \dfrac{210}{5}$

${\underline{\underline{\bf{ x= 42 }}}$

══════════════════════

➼ Finding value of ∠C and ∠D

∠C = 2x°

→ 2 × 42

= 84°

∠D = 3x°

→ 3 × 42

= 126°

∴ Angle C is 84° and D is 126°