The Triangle And Its Properties

Question

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Find the value of the unknowns x and y in the following diagrams:

Solution

(i) y + 120° = 180° (Linear pair)

y = 180° − 120º = 60º

x + y + 50° = 180° (Angle sum property)

x + 60° + 50° = 180°

x + 110° = 180°

x = 180° − 110° = 70°

(ii) y = 80° (Vertically opposite angles)

y + x + 50° = 180° (Angle sum property)

80° + x + 50° = 180°

x + 130º = 180°

x = 180° − 130º = 50°

(iii) y + 50° + 60° = 180° (Angle sum property)

y = 180° − 60° − 50° = 70°

x + y = 180° (Linear pair)

x = 180° − y = 180° − 70° = 110°

(iv) x = 60º (Vertically opposite angles)

30° + x + y = 180°

30° + 60° + y = 180°

y = 180° − 30° − 60° = 90°

(v) y = 90° (Vertically opposite angles)

x + x + y = 180° (Angle sum property)

2x + y = 180°

2x + 90° = 180°

2x = 180° − 90° = 90°

$x = \frac{90 °}{2} = 45 °$

(vi)

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y = x (Vertically opposite angles)

a = x (Vertically opposite angles)

b = x (Vertically opposite angles)

a + b + y = 180° (Angle sum property)

x + x + x = 180°

3x = 180°

$x = \frac{180 °}{3} = 60 °$

y = x = 60°

Some More Questions From The Triangle and its Properties Chapter

Draw rough sketches for the following:
(a) In ΔABC, BE is a median.
(b) In ΔPQR, PQ and PR are altitudes of the triangle.
(c) In ΔXYZ, YL is an altitude in the exterior of the triangle

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The Triangle And Its Properties

Find the value of the unknowns x and y in the following diagrams:

Some More Questions From The Triangle and its Properties Chapter

Draw rough sketches for the following:
(a) In ΔABC, BE is a median.
(b) In ΔPQR, PQ and PR are altitudes of the triangle.
(c) In ΔXYZ, YL is an altitude in the exterior of the triangle

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Find the value of the unknown exterior angle x in the following diagrams:

Find the value of the unknown interior angle x in the following figures:

Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm
(iii) 6 cm, 3 cm, 2 cm

Take any point O in the interior of a triangle PQR. Is
(i) OP + OQ > PQ?
(ii) OQ + OR > QR?
(iii) OR + OP > RP?

AM is a median of a triangle ABC.
Is AB + BC + CA > 2 AM?
(Consider the sides of triangles ΔABM and ΔAMC.)

ABCD is quadrilateral.
Is AB + BC + CD + DA >AC + BD?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

The Triangle And Its Properties

Find the value of the unknowns x and y in the following diagrams:

Some More Questions From The Triangle and its Properties Chapter

Draw rough sketches for the following:(a) In ΔABC, BE is a median.(b) In ΔPQR, PQ and PR are altitudes of the triangle.(c) In ΔXYZ, YL is an altitude in the exterior of the triangle

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Find the value of the unknown exterior angle x in the following diagrams:

Find the value of the unknown interior angle x in the following figures:

Is it possible to have a triangle with the following sides?(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm(iii) 6 cm, 3 cm, 2 cm

Take any point O in the interior of a triangle PQR. Is(i) OP + OQ > PQ?(ii) OQ + OR > QR?(iii) OR + OP > RP?

AM is a median of a triangle ABC.Is AB + BC + CA > 2 AM?(Consider the sides of triangles ΔABM and ΔAMC.)

ABCD is quadrilateral.Is AB + BC + CD + DA >AC + BD?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Draw rough sketches for the following:
(a) In ΔABC, BE is a median.
(b) In ΔPQR, PQ and PR are altitudes of the triangle.
(c) In ΔXYZ, YL is an altitude in the exterior of the triangle

Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm
(iii) 6 cm, 3 cm, 2 cm

Take any point O in the interior of a triangle PQR. Is
(i) OP + OQ > PQ?
(ii) OQ + OR > QR?
(iii) OR + OP > RP?

AM is a median of a triangle ABC.
Is AB + BC + CA > 2 AM?
(Consider the sides of triangles ΔABM and ΔAMC.)

ABCD is quadrilateral.
Is AB + BC + CD + DA >AC + BD?