If one angle of a triangle is equal to the sum of the other two angles, the triangle is
a. obtuse
b. acute
c. right
d. equilateral

Solution:

Given, one angle of a triangle is equal to the sum of the other two angles.

We have to find the type of the angle.

Consider a triangle ABC,

According to the question,

∠A = ∠B + ∠C ------------------------------ (1)

By angle sum property of a triangle,

We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.

So, ∠A + ∠B + ∠C = 180°

From (1),

∠A + ∠A = 180°

2∠A = 180°

∠A = 180°/2

∠A = 90°

Therefore, ABC is a right angled triangle.

✦ Try This: If one angle of a triangle is equal to the difference of the other two angles, the triangle is

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

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NCERT Exemplar Class 7 Maths Chapter 6 Problem 25

If one angle of a triangle is equal to the sum of the other two angles, the triangle is: a. Obtuse, b. Acute, c. right, d. equilateral

Summary:

If one angle of a triangle is equal to the sum of the other two angles, the triangle is right angled triangle

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☛ Related Questions:

• In Fig. 6.13, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is: a. 50°, b. 40°, c. 70°, d. 60°
• In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of . . . .
• In Fig. 6.11, the value of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F is: a. 190°, b. 540°, c. 360°, d. 180°