Q. 54.9( 24 Votes )
In the adjacent triangle ABC, find the value of x and calculate the measure of all the angles of the triangle.
Answer :
Given:
∠A = x + 15, ∠B = x - 15, ∠ C = x + 30
As we know, using theorem (1), in any triangle, sum of the three interior angles is 180°.
So,
∠A + ∠B + ∠ C = 180°
⇒ x +15 + x – 15 + x + 30 = 180°
⇒ 3x + 30° = 180°
⇒ 3x = 180° - 30°
⇒ 3x = 150°
⇒ x = 50°
So, the angles are,
∠A = x + 15 = 50° + 15° = 65°
∠B = x - 15 = 50° - 15° = 35°
∠ C = x + 30 = 50° + 30° = 80°
Rate this question :
Extras on Probability44 mins
NCERT | Imp. Qs. on Mensuration46 mins
Champ Quiz | Important Qs. on Petroleum30 mins
More on Calculation Hacks40 mins
Operations on Algebraic Expressions51 mins
NCERT | Discussion on Sound44 mins
NCERT | Discussion on Factorization44 mins
NCERT | Imp. Qs. on Percentage41 mins
Quiz | Rapid Fire on Sound31 mins
Quiz | Imp. Qs. on Light36 mins
In a triangle ABC, ∠B = 70°. Find ∠A + ∠C.
Karnataka Board - Mathematics Part IIn a triangle ABC, ∠A = 110° and AB = AC. Find ∠B and ∠C.
Karnataka Board - Mathematics Part IIn right angled triangle, ∠A is right angle and ∠B = 35°, then ∠C is _______
Karnataka Board - Mathematics Part IIn a triangle ABC, ∠A = 80° and AB = AC, then ∠B is ______
Karnataka Board - Mathematics Part IIn the figure, QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30°. Find ∠TRS and ∠PSQ.
In a triangle ABC, if 2∠A = 3∠B = 6∠C, determine ∠a, ∠B and ∠C.
Karnataka Board - Mathematics Part IIf three angles of a triangle are in the ratio 2:3:5, determine three angles.
Karnataka Board - Mathematics Part IThe angles of a triangle are x – 40°, x – 20° and x + 15°. Find the value of x.
Karnataka Board - Mathematics Part I