Question

OS. If two angles of a quadrilateral measure 60° and 90º and the remaining two are in the ratio 3:4. Find the remaining angles.​

Answer 1

Answer:

90° & 120°

Step-by-step explanation:

AS WE ALL KNOW THAT SUM OF ANGLES OF A QUADRILATERAL IS 360°

• <A+<B+<C+<D=360°
• 60°+90°+x+y=360°
• 150°+x+y=360°
• x+y=360°-150°
• x+y=210°
• X:Y = 3:4 = 210
• X=210×3/7 = 90°
• Y=210×4/7 = 120°

Answer 2

Given

• 1st angle = 90°
• 2nd angle = 60°
• Ratios = 3:4

To Find

• Find remaining angles = ?

Solution

We know that :

Sum of all angles of a quadrilateral is 360°.

Let :

3rd angle = 3x

4th angle = 4x

Solving starts :

${\leadsto{\sf{90° + 60° + 3x + 4x = 360°}}}$

${\leadsto{\sf{150° + 7x = 360°}}}$

${\leadsto{\sf{ 7x = 360° - 150°}}}$

${\leadsto{\sf{X = {\cancel \frac{210}{7} }}}}$

${\red{\underline{\bf{X = 30°}}}}$

Hence :

${\dag{\blue{\mathfrak{3rd \: angle = 3x = 3 × 30 = 90°}}}}$

${\dag{\blue{\mathfrak{4th \: angle = 4x = 4 × 30 = 120°}}}}$

For Varification :

${\twoheadrightarrow{\bf{Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360°}}}$

${\twoheadrightarrow{\bf{90° + 60° + 3x + 4x = 360°}}}$

${\twoheadrightarrow{\bf{90° + 60° + 3 × 30 + 4 × 30= 360°}}}$

${\twoheadrightarrow{\bf{90° + 60° + 90 + 120= 360°}}}$

${\mapsto{\pmb{\red{\sf{360° = 360° }}}}}$

${\mapsto{\pmb{\red{\sf{LHS = RHS }}}}}$

$\: \: \: \: \: \: \: \: \: \: \: {\orange{\underbrace{\underline{\sf{\red{Hence ,Varified}}}}}}$

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