Ncert solutions

Ncert solutions

Grade 7

The Triangle and its properties | Exercise 6.3

Question 1

Q1) Find the value of the unknown x in the following diagrams:

Solution 1:

(i) By using angle sum property of triangle

\angle A+\angle B+\angle C\ =\ 180\degree

x+50\degree+60\degree=\ 180\degree

x\ =\ 180\degree-\ 110\degree

x\ =\ 70\degree

(ii) By using angle sum property of triangle

\angle P+\angle Q+\angle R=\ 180\degree

90\degree+30\degree+x\ =\ 180\degree

x=\ 180\degree-120\degree

x\ =\ 60\degree

(iii) By using angle sum property of triangle

\angle X+\angle Y+\angle Z\ =\ 180\degree

30\degree+\ 110\degree+x=\ 180\degree

x\ =\ 180\degree-140\degree

x\ =\ 40\degree

(iv) By using angle sum property of triangle

\angle A+\angle B+\angle C=\ 180\degree

50\degree+\ x+x\ =\ 180\degree

50\degree+\ 2x\ =80\degree

x\ =\ \frac{130}{2}

x\ =\ 65\degree

(v) By using angle sum property of triangle

\angle A+\angle B+\angle C=\ 180\degree

x\ +x+x\ =\ 180\degree

\ 3x\ =\ 180\degree

x\ =\ \frac{180}{3}

x\ =\ 60\degree

(vi) By using angle sum property of triangle

\angle A+\angle B+\angle C\ =\ 180\degree

2x\ +90\degree+x\ =\ 180\degree

3x\ =\ 180\degree-90\degree

x\ =\ \frac{90}{3}

x=\ 30\degree

\angle A\ =\ 2x\ =\ 2\times30\ =60\degree

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subject-cta

Question 1

Q1) Find the value of the unknown x in the following diagrams:

Solution 1:

(i) By using angle sum property of triangle

\angle A+\angle B+\angle C\ =\ 180\degree

x+50\degree+60\degree=\ 180\degree

x\ =\ 180\degree-\ 110\degree

x\ =\ 70\degree

(ii) By using angle sum property of triangle

\angle P+\angle Q+\angle R=\ 180\degree

90\degree+30\degree+x\ =\ 180\degree

x=\ 180\degree-120\degree

x\ =\ 60\degree

(iii) By using angle sum property of triangle

\angle X+\angle Y+\angle Z\ =\ 180\degree

30\degree+\ 110\degree+x=\ 180\degree

x\ =\ 180\degree-140\degree

x\ =\ 40\degree

(iv) By using angle sum property of triangle

\angle A+\angle B+\angle C=\ 180\degree

50\degree+\ x+x\ =\ 180\degree

50\degree+\ 2x\ =80\degree

x\ =\ \frac{130}{2}

x\ =\ 65\degree

(v) By using angle sum property of triangle

\angle A+\angle B+\angle C=\ 180\degree

x\ +x+x\ =\ 180\degree

\ 3x\ =\ 180\degree

x\ =\ \frac{180}{3}

x\ =\ 60\degree

(vi) By using angle sum property of triangle

\angle A+\angle B+\angle C\ =\ 180\degree

2x\ +90\degree+x\ =\ 180\degree

3x\ =\ 180\degree-90\degree

x\ =\ \frac{90}{3}

x=\ 30\degree

\angle A\ =\ 2x\ =\ 2\times30\ =60\degree

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