Question

*The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are ……………..*

1️⃣ 45°, 75°
2️⃣ 50°, 80°
3️⃣ 85°, 55°
4️⃣ 55°, 95°

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Answer 1

❂Given:-

• First angle of triangle = x°

• Second angle of triangle = y°

• Third angle of triangle = 40°

• Difference between x and y = 30°

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❂To Find:-

• Value of x

• Value of y

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❂Property Used:-

• Sum of all of triangle is 180°

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❂Solution:-

According to property of triangle;

First angle + Second angle + third angle = 180°

➟ x + y + 40° = 180°

➟ x + y = 180° - 40°

➟ x + y = 140° -------------- eq. ①

According to given conditions;

➟ x - y = 30° ---------------- eq. ②

Sum of eq. ① and eq. ②

➟ x + y + ( x - y ) = 140° + 30°

➟ x + y + x - y = 170°

➟ x + x + y - y = 170°

➟ 2x + 0 = 170°

➟ x = 170 ÷ 2

➟ x = 85°

∴ x = 85°

Substituting value of x in eq. ①

x + y = 140°

➟ 85 + y = 140°

➟ y = 140 - 85

➟ y = 55°

∴ y = 55°

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❂Answer:-

• Value of x = 85°
• Value of y = 55°

Option 3 is correct.

1️⃣ 45°, 75°

2️⃣ 50°, 80°

3️⃣ 85°, 55°✅

4️⃣ 55°, 95°

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