Question

Clear sele
A triangle PQR is right angled at R.
If angle P measures 3x and angle Q
measures 2x, the value of x is​

Answer 1

Answer :–

• Value of x = 18°

Given :–

• A triangle PQR.
• ∠R = 90°
• ∠P = 3x
• ∠Q = 2x

To Find :–

• Value of x.

Solution :–

We know that,

Sum of all the three angles of a triangle is 180°.

So,

We have all the three angles,

• ∠P = 3x
• ∠Q = 2x
• ∠R = 90° [right angle]

Put this values in the given formula,

⟹ ∠P + ∠Q + ∠R = 180°

⟹ 3x + 2x + 90° = 180°

⟹ 5x + 90° = 180°

⟹ 5x = 180° – 90°

⟹ 5x = 90°

⟹ x = $\dfrac{\cancel{90}°}{\cancel{5}}$

Now, cut the denominator (5) and the numerator (90) by 5, we obtain

⟹ x = 18°

Hence,

• The value of x = 18°

And the angles are,

• ∠P = 3x = 3 × 18° = 54°
• ∠Q = 2x = 2 × 18° = 36°