Question

Help me in math it is urgent​

Answer 1

${\large{\bf{\clubs{\red{\underline{Solutions :}}}}}}$

7.The angles of a quadrilateral are in the ratio 2:3:4:9 .what is the measure of smallest angle :

Sol 1.

${\purple{\sf{Let \: the \: ratio \: be \: x :}}}$

${\sf{\green{2x + 3x + 4x + 9x = 360°}}}$

${\sf{\green{18x = 360°}}}$

${\sf{\green{x ={\cancel \frac{360}{18} = 20 }}}}$

Now,

${\bf{\red{2x = 2 \times 20 = 40°}}}$

${\bf{\red{3x = 3 \times 20 = 60°}}}$

${\bf{\red{4x = 4 \times 20 = 80°}}}$

${\bf{\red{9x = 9 \times 20 = 180°}}}$

So,

${\tt{\green{The \: measure \: of \: smallest \: angle \: is \: 40°.}}}$

8.The angles A, B, C and D of a quadrilateral ABCD are in ratio 1:3:7:9 ,than ABCD is a :

Sol 8.

${\sf{\purple{Let \: t he \: ratio \: be \: x :}}}$

${\sf{\green{1x + 3x + 7x + 9x = 360°}}}$

${\sf{\green{20x = 360°}}}$

${\sf{\green{x ={\cancel \frac{360}{20} = 18 }}}}$

Than,

${\sf{\red{1x = 1 \times 18 = 18°}}}$

${\sf{\red{3x = 3 \times 18 = 54°}}}$

${\sf{\red{7x = 7 \times 18 = 126°}}}$

${\sf{\red{9x = 9 \times 18 = 162°}}}$

So,

${\tt{\green{It's \: a \: parallelogram. }}}$

Answer 2

$\bf{\pmb{\mathbb{\fbox{\red{Given:}}}}}$

12. In a parallelogram ABCD, the bisector of ∠A and ∠B meet at E. Then, ∠AEB = ?

$\bf{\pmb{\mathbb{\fbox{\red{Solution:}}}}}$

ABCD is a parallelogram

${\bf{\blue{⇒ ∠A+∠B=180⁰}}}$

[Sum of adjacent angles of parallelogram are supplementary]

$\bf{\purple{⇒ \frac{1}{2}∠A + \frac{1}{2}∠B= \frac{180⁰}{2} }}$

${\bf{\purple{⇒ ∠OAB+∠OBA=90⁰}}}$

${\bf{\pmb{\text{In △AOB}}}}$

${\bf{\orange{⇒ ∠OAB + ∠AOB + ∠OBA = 180⁰}}}$

${\bf{\orange{⇒ ∠AOB=180⁰ − (∠OAB+∠OBA)}}}$

${\bf{\orange{⇒ ∠AOB=180⁰ - 90⁰}}}$

${\bf{\green{∴ ∠AOB=90⁰}}}$

$\bf{\pmb{\mathbb{\fbox{\red{Hope it's help you}}}}}$