Question

Q.2.A. The angles of a quadrilateral are in the following ratio. Find the
measurements of the angles.

a) 2:3:4:6​

Answer 1

Answer:

Given :-

• The angles of a quadrilateral are in the ratio of 2 : 3 : 4 : 6.

To Find :-

• What is the measurement of the angles.

Solution :-

Let,

➢ First angle = 2x

➢ Second angle = 3x

➢ Third angle = 4x

➢ Fourth angle = 6x

As we know that :

★ Sum of the all angles of a quadrilateral = 360° ★

According to the question by using the formula we get,

↦ 2x + 3x + 4x + 6x = 360°

↦ 5x + 10x = 360°

↦ 15x = 360°

↦ x = 360°/15

➠ x = 24°

Hence, the required angles of a quadrilateral are :

➲ First angle :

↦ 2x

↦ 2(24°)

↦ 2 × 24°

➦ 48°

➲ Second angle :

↦ 3x

↦ 3(24°)

↦ 3 × 24°

➦ 72°

➲ Third angle :

↦ 4x

↦ 4(24°)

↦ 4 × 24°

➦ 96°

➲ Fourth angle :

↦ 6x

↦ 6(24°)

↦ 6 × 24°

➦ 144°

∴ The measurements of the angles of a quadrilateral is 48° , 72° , 96° and 144° respectively.

_________________________

✪ VERIFICATION ✪

⇒ 2x + 3x + 4x + 6x = 360°

By putting x = 24° we get,

⇒ 2(24°) + 3(24°) + 4(24°) + 6(24°) = 360°

⇒ 48° + 72° + 96° + 144° = 360°

➤ 360° = 360°

Hence, Verified.

Answer 2

$\huge\bold\color{plum}answer-$

$\purple{ \star \: take \: the \: given \: ratios \: as \: x \: term}$

$\pink{ \hookrightarrow \: 2 \ratio \: 3 \ratio \: 4 \ratio \: 6 \:} \\ \blue{\dagger \: 2x } \\ \blue{ \dagger \: 3x} \\ \blue{ \dagger \: 4x }\\ \blue{ \dagger \: 6x}$

$\red{\circ \: sum \: of \: the \: angles \: of \: the \: quadrilateral \: = 360 \degree}$

$\orange{ \mapsto\: 2x + 3x + 4x + 6x = 360 \degree} \\ \orange{\longmapsto15x = 360 \degree }\\ \green {\star \: x = \frac{360}{15} = 24}$

$\green{ \: first \: \angle \: e = 2 \times 24 = 48 }$

$\green {\: second \: \angle \: e = 3 \times 24 =72}$

$\green{ \: third \:\angle \: e = 4 \times 24 = 96}$

$\green {\: fourth \: \angle \: e = 6 \times 24 = 144}$

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