If $(2 x + 5)^{\circ}$ , $3 x^{\circ}$ , $(5 x + 15)^{\circ}$ and $40^{\circ}$ are four angles of a quadrilateral, find the value of $∠ x$ and hence find the four angles.
[2 MARKS]

Open in App

Solution

Concept : 1 Mark
Calculation : 1 Mark

We know that in a quadrilateral,

$(2 x + 5) ° + 3 x ° + (5 x + 15) ° + 40 ° = 360 °$
[By angle sum property]

$10 x + 60 ° = 360 °$

$10 x = 300^{\circ}$

$x = 30^{\circ}$

Thus, the first angle is $2 x + 5 = 65^{\circ}$

Second angle is $3 x = 90^{\circ}$

Third angle is $5 x + 15 = 165^{\circ}$

The last angle is given as $40^{\circ}$

Suggest Corrections

Similar questions

A B C D

A = (6 x + 10)

B = (5 x)

C = (x + y)

D = (3 y - 10)

x

y

A B C D

∠ A = (6 x + 10)^{\circ}, ∠ B = (5 x)^{\circ}

∠ C = (x + y)^{\circ}, ∠ D = (3 y - 10)^{\circ}

x

y,

(2 x + 5)^{o}, (3 x - 5)^{o}, (x + 40)^{o}, (2 x + 20)^{o}, (2 x + 35)^{o}

x

Join BYJU'S Learning Program