Question

Angle a of quadrilateral abcd is 26 degrees less than angle b angle b is twice angle c and angle c is 10 degree more than angle d what would be the measures of angle a

Answer 1

please check the solution and this is correct

Answer 2

Answer:

The measures of angle A is 106°

Step-by-step explanation:

Let the measurement of angle D is x,

That is,

m∠D = (x)°,

Since, angle C is 10 degree more than angle D,

m∠C = (x + 10)°

And, angle B is twice angle C,

m∠B = 2(x+10)°

Also, Angle A is 26 degrees less than angle B,

m∠A = 2(x+10)°-26°

Here, ABCD is a quadrilateral,

We know that, the sum of all interior angles of a quadrilateral is 360°,

⇒ m∠A + m∠B + m∠C + m∠D = 360°

⇒ 2(x+10)°-26° + 2(x+10)°+ (x + 10)°+x = 360°,

⇒ 5(x+10)°+ x = 360° + 26° = 386°

⇒ 6x + 50° = 386°

⇒ 6x = 336°

⇒ x = 56°,

Hence,  the measure of angle A = 2(56+10)°-26°=2(66)°-26° = 132° - 26° = 106°