Question

The sum of the two angles of a quadrilayeral is 150°. The remaining two angles are in the ratio of 3:4, Find the angles​

Answer 1

120,90

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Answer 2

$\: \: \: \: \: \: \: \: \: \: \: {\Large{\underline{\overline{\bf{\red{Correct \: Question : }}}}}}$

The sum of the two angles of a Quadrilateral is 150°. The remaining two angles are in the ratio of 3:4, Find the angles.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\Large{\underline{\overline{\bf{\red{Answer : }}}}}}$

Given :-

• Sum of two angles of Quadrilateral is 150°.
• Remaining two angles are in ratio of 3 : 4.

To find :-

• We need to find measure of remaining two angles.

Assumption :-

• Assume that Ratio in the form of x as 3x and 4x.

Solution :-

A quadrilateral has four angles and sum of their their angles is 360°.

● So, Value of x is

${\large{\sf{\implies{150 \degree +3x + 4x = 360\degree }}}}$

${\large{\sf{\implies{150 \degree +7x = 360\degree }}}}$

${\large{\sf{\implies{7x = 360\degree - 150 \degree }}}}$

${\large{\sf{\implies{7x = 210 \degree }}}}$

${\large{\sf{\implies{x = \cfrac{ 210 \degree }{7} }}}}$

${\large{ \underline{ \overline{ \boxed{ \purple{\implies{ \bf{ {x = 30 \degree }}}}}}}}}$

● Unknown angles are :-

❶ Angle

${\large{\bf{\implies{3x}}}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\sf{\implies{3 \times 30 \degree}}}} \\ \\ \: \: \: { \pink{\large{\underline{\boxed{\bf{\implies{90 \degree}}}}}}}$

❷ Angle

${\large{\bf{\implies{4x}}}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\sf{\implies{4\times 30 \degree}}}} \\ \\ \: \: \: \: \: \: \: { \pink{{\large{\underline{\boxed{\bf{\implies{120 \degree}}}}}}}}$

_______________________

VERIFICATION

${\large{\sf{\implies{150 \degree + 90 \degree + 120 \degree = 360\degree }}}}$

${\large{\sf{\implies{150 \degree + 210\degree = 360\degree }}}}$

${\large{\sf{\implies{360\degree =360\degree }}}}$

LHS = RHS

Hence, our answer as value of x is correct and Measue of two angles are correct.