Advertisements
Advertisements
प्रश्न
In the given figure, find the values of x, y and z.
उत्तर
In the give figure, ∠BAD = 60°, ∠ABD = 60°, ∠ADB = x, ∠DAC = 30°, ∠ADC = y and ∠ACD = z
We know that, the sum of all angles in a triangle is equal to 180°
In ΔABD, ∠BAD + ∠ABD + ∠ADB = 180°
⇒ 60° + 60° + x = 180°
⇒ 120° + x = 180°
⇒ x = 180° – 120°
⇒ x = 60°
Now, y = ∠BAD + ∠ABD ......[∵ Exterior angle is equal to the sum of interior opposite angles]
⇒ y = 60° + 60°
∴ y = 120°
In ΔADC, ∠DAC + ∠ADC + ∠ACD = 180° ......[Angle sum property of a triangle]
⇒ 30° + 120° + z = 180°
⇒ 150° + z = 180°
⇒ z = 180° – 150°
⇒ z = 30°
Hence, x = 60°, y = 120° and z = 30°.
APPEARS IN
संबंधित प्रश्न
In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.
Find the value of the unknown x and y in the following diagram:
In the following triangle, find the value of x
If ∆MNO ≅ ∆DEF, ∠M = 60° and ∠E = 45° then find the value of ∠O
A triangle ABC is right angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL = ∠ACB.
If two angles of a triangle are 60° each, then the triangle is ______.
In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.
In the given figure, find the measures of ∠x and ∠y.
In ∆ABC, DE || BC (see figure). Find the values of x, y and z.
In ΔDEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find (i) ∠F (i) ∠EOF.
