Question

I neeed Help pls im stuck on this question.

Answer 1

`x = 12`

Explanation:

A right angled triangle is given to us and we need to find out the value of " x " . The two unknown angles are (2x + 1)° and (5x + 5)° .

We know that, the Angle sum property of a triangle is 180° . So the sum of all the given angles inside the triangle will be 180° .

And as per question one of the angle is 90° . So the sum of other two angles will be 90° .

Hence ,

2x + 1 + 5x + 5 + 90 = 180

7x + 96 = 180

7x = 180 - 96

7x = 84

x = 84/2

x = 12

Hence the value of x is 12 .

And we are done!

Answer 2

x = 12

The sum of ∠A and ∠C is 90°.

Explanation:

Interior angles of a triangle sum to 180°.

`\implies m \angle A + m \angle B + m \angle C = 180^(\circ)`

From inspection of the given right triangle:

• m∠A = (2x + 1)°
• m∠B = 90°
• m∠C = (5x + 5)°

Substitute the given angles into the equation and solve for x:

`\implies m \angle A + m \angle B + m \angle C = 180^(\circ)`

`\implies (2x+1)^(\circ) + 90^(\circ) + (5x+5)^(\circ) = 180^(\circ)`

`\implies (2x+1)^(\circ) + 90^(\circ) + (5x+5)^(\circ)-90^(\circ) = 180^(\circ)-90^(\circ)`

`\implies (2x+1)^(\circ) + (5x+5)^(\circ) = 90^(\circ)`

`\implies 2x+1 + 5x+5 = 90`

`\implies 2x+ 5x+1 +5 = 90`

`\implies 7x+6 = 90`

`\implies 7x+6 -6= 90-6`

`\implies 7x=84`

`\implies 7x/7=84/7`

`\implies x=12`

Therefore, the value of x is 12.

To find the measure of each angle, substitute the found value of x into the expression for each angle:

• 
  `m \angle A=(2(12)+1)^(\circ)=25^(\circ)`

• 
  `m \angle B=90^(\circ)`

• 
  `m \angle C=(5(12)+5)^(\circ)=65^(\circ)`