Question

Find the measure of ∠D if

∠A =
5
2
x + 16
∠B =
7
2
x + 20
∠C =
3
2
x + 68
∠D =
3
2
x + 40

Answer 1

Sum of all Angles of a quadrilateral=360

Ang.A + Ang.B+ Ang.C + Ang.D =360
=> (52x + 16) + (72x + 20)
+ ( 32x + 68) + (32x + 40)=360
=> 188x= 216
> x = 1.1489

Ang.D=32 X 1.1489+ 40= 76.7648

Answer 2

Considering the Quadrilateral ABCD as convex Quadrilateral

→ The Sum of angles of any Quadrilateral is 360°.

→∠A +∠B +∠C +∠D= 360°

→52 x + 16° + 72 x + 20° + 32 x +68°+ 32 x +40° = 360°

Adding the term containing variables separately and the constant terms separately

→ (52 x + 72 x +32 x+32 x) + (16° +20°+68°+40°)=360°

→ 188 x + 144°=360°

→ 188 x = 360°-144°

→ 188 x= 216°

→x=
`(216)/(188)=(54)/(47)`

∠D= 32 ×
`(54)/(47)` +40

∠D=36.765 +40= 76.765 (approx)