Question

In a quadrilateral ABCD, the angles A, B, C, D are in the ratio 13: 4: 5: 8. Find the measure of the angle B of that quadrilateral.​

Answer 1

we know that sum of interior angles of quadrilateral is 360.

Let take the number as X

Then angles A,B,C,D =13x,4x,5x,8x

Sum of angles = 13x+4x+5x+8x=360

=30x=360

X=12

Then measure of angle B is 4(12)=48°

Step-by-step explanation:

Answer 2

Given : Ratio of the angles of a Quadrilateral are 13:4:5:8 .

To Find : Find the Measure of ∠B

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SolutioN : First we'll assume the Ratios and by solving it we can get the Angles . Let's Solve :

$\maltese \; {\underline{\textbf{\textsf{ Let \; the \; Ratios \; :- }}}}$

• ∠A = 13y
• ∠B = 4y
• ∠C = 5y
• ∠D = 8y

$\maltese \; {\underline{\textbf{\textsf{ We \; Know \; That \; :- }}}}$

• ${\underline{\boxed{\pmb{\sf{ Sum \; of \; Angles{\small_{(Quadrilateral)}} = 360° }}}}}$

$\maltese \; {\underline{\textbf{\textsf{ Calculating \; the \; Value \; of \; y \; :- }}}}$

${\dashrightarrow{\qquad{\sf{ ∠A + ∠B + ∠C + ∠D = 360° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 13y + 4y + 5y + 8y = 360° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 17y + 13y = 360° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 30y = 360° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \dfrac{360}{30} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \cancel\dfrac{360}{30} }}}} \\ \\ \\ \ {\qquad \; \; {\dashrightarrow{\underline{\boxed{\pmb{\frak{ y = 12 }}}}}}} \; {\red{\bigstar}}$

$\maltese \; {\underline{\textbf{\textsf{ Calculating \; the \; Angles \; :- }}}}$

• ∠A = 13y = 13(12) = 156°
• ∠B = 4y = 4(12) = 48°
• ∠C = 5y = 5(12) = 60°
• ∠D = 8y = 8(12) = 96°

$\therefore \; \;$ Second Angle of the Quadrilateral is 48° .

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