Advertisements
Advertisements
Question
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.
Solution
According to the question,
Measure of ∠A = ∠B = 40°
Measure of ∠C = ∠B – 40° + 50°
We know that, the sum of all three angles in a triangle is equal to 180°
i.e. ∠A + ∠B + = 180°°
⇒ (∠B – 40°) + ∠B + (∠B – 40° + 50°) = 180°
⇒ 3∠B – 30° = 180°
⇒ 3∠B = 210°
∴ ∠B = `210^circ/3` = 70°
So, the measure of ∠A = 70° – 40° = 30°.
APPEARS IN
RELATED QUESTIONS
In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR = 1/2∠QPR.
Find the value of the unknown x in the following diagram:
Find the value of the unknown x and y in the following diagram:
In ∆RST, ∠S is 10° greater than ∠R and ∠T is 5° less than ∠S, find the three angles of the triangle
If ∆MNO ≅ ∆DEF, ∠M = 60° and ∠E = 45° then find the value of ∠O
In a right-angled triangle, the angles other than the right angle are ______.
In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B is equal to ______.
It is possible to have a triangle in which each angle is greater than 60°.
In the given figure, find the measures of ∠PON and ∠NPO.
In ΔDEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find (i) ∠F (i) ∠EOF.
