Question

6. find the interior angles of a triangle if they are in the ratio.
(a) 1:3:1
(b) 1:1:2
(c) 2:2:2
(d) 2:3:4
this is the question of subject Math chapter name Triangles and their properties of standard 7 ​

Answer 1

Answer:

a) 36, 108 and 36 are the interior sides of the triangle.

b) 45, 45 and 90 are the interior sides of the triangle.

c) 60, 60 and 60 are the interior sides of the triangle.

d) 40, 60 and 80 are the interior sides of the triangle.

Answer 2

$Solution \:(a) :$

Given :-

The ratio of the measures of the interior angles of a triangle =1:3:1

Sum of all angles = 180°(angle sum property)

Which means :-

Angle one :-

$= \frac{\texttt{1}}{\texttt{5}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{1}}{\texttt{5} }\texttt{ \: × \: 180}$

$= \frac{\texttt{1×180}}{\texttt{5} }$

$= \frac{\texttt{180}}{\texttt{5} }$

$=\texttt{\color{hotpink}36}\color{hotpink}°$

Thus, the measure of the first angle = 36°

Angle two :-

$= \frac{\texttt{3}}{\texttt{5}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{3}}{\texttt{5}} \texttt{ \: × 180}$

$= \frac{\texttt{3×180}}{\texttt{5} }$

$= \frac{\texttt{540}}{\texttt{5} }$

$=\color{hotpink} \texttt{108}°$

Thus, the measure of the second angle = 108°

Angle three :-

$= \frac{\texttt{1}}{\texttt{5} } \: \texttt{ \: of \: 180}$

$= \frac{\texttt{1}}{\texttt{5}} \texttt{ \: × \: 180}$

$= \frac{\texttt{1×180}}{\texttt{5} }$

$= \frac{\texttt{180}}{\texttt{5} }$

$=\texttt{\color{hotpink}36}\color{hotpink}°$

Thus, the measure of the third angle = 36°

Therefore, the measure of the three interior angles of this triangle are =36°, 36° and 108°.

$Solution \:(b) :$

Given :-

The ratio of the measures of the interior angles of a triangle =1:1:2

Sum of all angles = 180°(angle sum property)

Which means :-

Angle one :-

$= \frac{\texttt{1}}{\texttt{4}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{1}}{\texttt{4} }\texttt{ \: × \: 180}$

$= \frac{\texttt{1×180}}{\texttt{4} }$

$= \frac{\texttt{180}}{\texttt{4} }$

$=\color{hotpink} \texttt{45}°$

Thus, the measure of the first angle = 45°

Angle two :-

$= \frac{\texttt{1}}{\texttt{4}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{1}}{\texttt{4} }\texttt{ \: × \: 180}$

$= \frac{\texttt{1×180}}{\texttt{4} }$

$= \frac{\texttt{180}}{\texttt{4} }$

$=\color{hotpink} \texttt{45}°$

Thus, the measure of the second angle = 45°

Angle three :-

$= \frac{\texttt{2}}{\texttt{4}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{2}}{\texttt{4}} \texttt{ \: × \: 180}$

$= \frac{\texttt{2×180}}{\texttt{4} }$

$= \frac{\texttt{360}}{\texttt{4} }$

$= \color{hotpink}\texttt{90}°$

Thus, the measure of the third angle =90°

Therefore, the measure of each angles of this triangle are = 45°, 45° and 90° .

$Solution \:(c) :$

Given :-

The ratio of the measures of the interior angles of a triangle = 2:2:2

Sum of the measure of all the angles =180°(angle sum property)

Which means :-

Angle one :-

$= \frac{\texttt{2}}{\texttt{6}} \:\texttt{ of \: 180}$

$= \frac{\texttt{2}}{\texttt{6}} \: \texttt{ \: × \: 180}$

$= \frac{\texttt{2×180}}{\texttt{6}}$

$= \frac{\texttt{360}}{\texttt{6} }$

$=\color{hotpink} \texttt{60}°$

Thus, the measure of the first angle = 60°

Angle two :-

$= \frac{\texttt{2}}{\texttt{6}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{2}}{\texttt{6}}\texttt{ \: × \: 180}$

$= \frac{\texttt{2×180}}{\texttt{6} }$

$= \frac{\texttt{360}}{\texttt{6} }$

$=\color{hotpink} \texttt{60}°$

Thus, the measure of the second angle = 60°

Angle three :-

$= \frac{\texttt{2}}{\texttt{6}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{2}}{\texttt{6}}\texttt{ \: × \: 180}$

$= \frac{\texttt{2×180}}{\texttt{6} }$

$= \frac{\texttt{360}}{\texttt{6} }$

$=\color{hotpink} \texttt{60}°$

Therefore, the measure of the three interior angles of a triangle are = 60° , 60° and 60°

$Solution \:(d) :$

Given :-

The ratio of the measures of the interior angles of a triangle =2:3:4

Sum of all these angles =180°(angle sum property)

Which means :-

Angle one :-

$= \frac{\texttt{2}}{\texttt{9}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{2}}{\texttt{9} } \texttt{\: \: \: × \: 180}$

$= \frac{\texttt{2×180}}{\texttt{9} }$

$= \frac{\texttt{360}}{\texttt{9} }$

$=\color{hotpink}\texttt{40}°$

Thus the measure of the first angle = 40°

Angle two :-

$= \frac{\texttt{3}}{\texttt{9}} \texttt{\: \: \: of \: 180}$

$= \frac{\texttt{3}}{\texttt{9}} \texttt{ \: × \: 180}$

$= \frac{\texttt{3×180}}{\texttt{9} }$

$= \frac{\texttt{540}}{\texttt{9} }$

$=\color{hotpink} \texttt{60}°$

Thus, the measure of the second angle =60°

Angle three :-

$= \frac{\texttt{4}}{\texttt{9}} \:\texttt{ of \: 180}$

$= \frac{\texttt{4}}{\texttt{9}}\texttt{ \: × \: 180}$

$= \frac{\texttt{4×180}}{\texttt{9}}$

$= \frac{\texttt{720}}{\texttt{9} }$

$=\color{hotpink}\texttt{80}°$

Thus, the measure of the third angle =80°

Therefore, the measure of each of the angles of this triangle are = 40°,60° and 80°