# RS Aggarwal Solutions for Class 7 Maths Exercise 15A Chapter 15 Properties of Triangles

RS Aggarwal Solutions for Class 7 Maths Exercise 15A Chapter 15 Properties of Triangles, Download PDF are given here. This exercise of RS Aggarwal Solutions for Class 7 Maths Chapter 15 contains questions related to various types of triangles and angle sum property of a triangle. We at Byju’s have prepared the solutions with stepwise containing neat descriptions. Students can score more marks in Maths by practising RS Aggarwal Solutions for Class 7 Maths Chapter 15 Properties of Triangles.

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### Access answers to Maths RS Aggarwal Solutions for Class 7 Chapter 15 – Properties of Triangles Exercise 15A

1. In a Î”ABC, if âˆ A = 72o and âˆ B = 63o, find âˆ C.

Solution:-

We know that the sum of the angles of a triangle is 180o.

âˆ´ âˆ A + âˆ B + âˆ C = 180o

= 72o+ 63o+ âˆ C = 180o

= 135o + âˆ C = 180o

= âˆ C = 180o– 1350

= âˆ C = 45o

Hence, the measures of âˆ C is 45o.

2. In a Î”DEF, if âˆ E = 105o and âˆ F = 40o, find âˆ D.

Solution:-

We know that the sum of the angles of a triangle is 180o.

âˆ´ âˆ D + âˆ E + âˆ F = 180o

= âˆ D + 105o+ 40o = 180o

= 145o + âˆ D = 180o

= âˆ D = 180o– 1450

= âˆ D = 35o

Hence, the measures of âˆ D is 35o.

3. In a Î”XYZ, if âˆ X = 90o and âˆ Z = 48o, find âˆ Y.

Solution:-

We know that the sum of the angles of a triangle is 180o.

âˆ´ âˆ X + âˆ Y + âˆ Z = 180o

= 90o + âˆ Y + 48o = 180o

= 138o + âˆ Y = 180o

= âˆ Y = 180o– 1380

= âˆ Y = 42o

Hence, the measures of âˆ Y is 42o.

4. Find the angles of a triangle which are in the ratio 4: 3: 2.

Solution:-

Let the measures of the given angles of the triangles be (4x)o, (3x)o and (2x)o respectively.

Then,

= 4x + 3x + 2x = 180o â€¦ [âˆµsum of the angles of a triangle is 180o]

= 9x = 180o

= x = 180/9

= x = 20

So, the angle measures (4 Ã— 20)o, (3 Ã— 20)o, (2 Ã— 20)o,

i.e., 80o, 60o, 40o.

Hence, the angles of the triangles are 80o, 60o, 40o.

5. One of the acute angles of right triangle is 36o, find the other.

Solution:-

Let the three angles be âˆ A, âˆ B, âˆ C

And,

âˆ A = 36o

âˆ B = 90o

[âˆµfrom the question the given triangle is a right angled triangle. In this one of the angle is equal to 90o]

âˆ C = x

Now,

= âˆ A + âˆ B + âˆ C = 180o â€¦ [âˆµsum of the angles of a triangle is 180o]

= 36o + 90o + âˆ C = 180o

= 126o + âˆ C = 1800

= âˆ C = 180o â€“ 126o

= âˆ C = 54o

Hence, the other angle is 54o.

6. The acute angle of a right triangle are in the ratio 2: 1. Find each of these angles.

Solution:-

Let the three angles be âˆ A, âˆ B, âˆ C

And,

âˆ A = 2xo

âˆ B = 1xo

âˆ C = 90o

[âˆµfrom the question the given triangle is a right angled triangle. In this one of the angle is equal to 90o]

Now,

= âˆ A + âˆ B + âˆ C = 180o â€¦ [âˆµsum of the angles of a triangle is 180o]

= 2xo + xo + 90o = 180o

= 3xo = 1800– 90o

= 3xo = 90o

= xo = 90o/3

= xo = 30

Now, substitute the value of x in the given angles.

âˆ A = 2xo = 2 Ã— 30 = 60o

âˆ B = 1xo= 1 Ã— 60 = 30o

Hence, the other angles are 60o and 30o.

7. One of the angles of a triangle is 100o and the other two angles are equal. Find each of the equal angles.

Solution:-

Let the other two equal angles be x.

Then,

= x + x + 100o = 180o â€¦ [âˆµsum of the angles of a triangle is 180o]

= 2x = 180o â€“ 100o

= 2x = 80o

= x = 80o/2

= x = 40o

Hence, the other two equal angles are 40o and 40o.

### Access other exercises of RS Aggarwal Solutions For Class 7 Chapter 15 – Properties of Triangles

Exercise 15B Solutions

Exercise 15C Solutions

Exercise 15D Solution