Question

In a right triangle, apart from the right angle, the other two angles are x + 1 and 2x + 5. Find the angles of the triangle.

Answer 1

$\huge\sf\pink{Answer}$

☞ ∠BAC = 29°

☞ ∠BCA = 61°

━━━━━━━━━━━━━

$\huge\sf\blue{Given}$

✭ ABC is a right triangle

✭ The other two angles are x+1 & 2x+5

━━━━━━━━━━━━━

$\huge\sf\gray{To \:Find}$

◈ The other two Angles?

━━━━━━━━━━━━━

$\huge\sf\purple{Steps}$

So we know that in a triangles add up to 90° so,here

◕ ∠BAC = x+1

◕ ∠BCA = 2x+5

◕ ∠ABC = 90°

Then,

➝ $\sf \angle BAC + \angle BCA + \angle ABC = 180^{\circ}$

Substituting the values,

➝ $\sf (x+1) + (2x+5) + 90^{\circ} = 180^{\circ}$

➝ $\sf x+1+2x+5+90^{\circ} =180^{\circ}$

➝ $\sf 3x+96 = 180^{\circ}$

➝ $\sf 3x = 180-96$

➝ $\sf 3x = 84$

➝ $\sf x = \dfrac{84}{3}$

➝ $\sf x = 28$

So then the other 2 Angles are,

»» ∠BAC = x+1 = 28+1 = 29°

»» ∠BCA = 2x+5 = 2(28)+5 = 61°

━━━━━━━━━━━━━━━━━━

Answer 2

Given:

A right angled triangle

One angle will be 90 since it is a right angled triangle.

Second angle of the triangle = x + 1

Third angle of the triangle = 2x + 5

If you add all the angles of the triangle then the sum will be = 180

To Find:

The measure of the two angles of the right angled triangle

Calculating:

Adding the all the angles together:

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

=> 3x + 6 + 90 = 180

=> 96 + 3x = 180

Taking 96 to the other side of the equation we get:

=> 3x = 180 - 96

=> 3x = 84

Taking 3 to the other side of the equation we get:

=> x = 84/3

=> x = 28

Therefore, the value we obtain for 'x' is 28.

Calculating the measure of second angle:

= x + 1

Putting value we obtained for 'x':

= 28 + 1

= 29°

Therefore, the measure of the second angle is 29°.

Calculating the measure of third angle:

= 2x + 5

Putting value we obtained for 'x':

= 2 x 28 + 5

= 56 + 5

= 61°

Therefore, the measure of the third angle is 61°.