2. FI
1. Find the measures of each of the unknown angles denoted by the letters of English alphabet
(c)
(a)
(b)
50-
700
210
Answers
Answer:
Solution (a) :</p><p>
Measure of the first angle of this triangle = 19°
Measure of the second angle of this triangle = 21°
Measure of the third angle = x
Then :-
according to angle sum property :-
= \texttt{∠}x \texttt{ \: + 19 + 21 = 180}=∠x + 19 + 21 = 180
= \texttt{∠}x \texttt{ \: + 40 \: = 180}=∠x + 40 = 180
= ∠x \texttt{ \: = 180 - 40}=∠x = 180 - 40
= \color{hotpink}∠x\texttt{ = 140}°=∠x = 140°
Now let us check whether or not we have found out the correct measure of x by placing 140 in the place of x :-
=\texttt{ 140 + 19 + 21 = 180}= 140 + 19 + 21 = 180
= \texttt{180 = 180}=180 = 180
As the measure of all three interior angles of this triangle is adding up to 180°, we can conclude that we have found out the correct measure of the unknown angle x .
Therefore, the measure of the unknown angle x = 140°
\texttt{\color{olive}Solution (b) :}Solution (b) :
Measure of the first angle = 50°
Measure of the second angle = x
Measure of the third angle = x
Their sum = 180° ( angle sum property )
Which means :-
= \texttt{50} \texttt{ \: + \: } x \texttt{ \: + \: } x \texttt{ \: = 180}=50 + x + x = 180
= \texttt{50} \texttt{ \: + \: 2}x \texttt{ \: = 180}=50 + 2x = 180
= \texttt{2}x \texttt{ \: = 180 - 50}=2x = 180 - 50
=\texttt{ 2}x \texttt{ \: = 130}= 2x = 130
= x \texttt{ \: = \: } \frac{\texttt{130}}{\texttt{2} }=x =
2
130
=\color{hotpink} ∠x \texttt{ \: = \: 65}°=∠x = 65°
Now let us check whether or not we have found out the correct measure of x by placing 65 in the place of x :-
= \texttt{50 + 65 + 65 = 180}=50 + 65 + 65 = 180
=\texttt{180 = 180}=180 = 180
As the measure of the unknown angle and the other interior angles of this triangle is adding up to 180°, we can conclude that we have found out the correct value of x .
Therefore, the measure of the unknown angle x = 65°
\texttt{\color{olive}Solution (c) :}Solution (c) :
Measure of the first angle = 40°
Measure of the second angle = 90°
Measure of the third angle = a
The sum of all these three angles = 180°(angle sum property)
Which means :-
= \texttt{40 + 90 + a = 180}=40 + 90 + a = 180
= \texttt{130 + a = 180}=130 + a = 180
= a \texttt{ \: = \: 180 - 130}=a = 180 - 130
= \texttt{\color{hotpink}∠a \: \: = \: 50}\texttt{}\color{hotpink}°=∠a = 50°
Now let us check whether or not we have found out the correct measure of a by placing 50 in the place of a :-
= \texttt{40 + 90 + 50 = 180}=40 + 90 + 50 = 180
=\texttt{ 180 \: = \: 180}= 180 = 180
As the measure of the unknown angle we have found out and the other interior angles of this triangle is adding up to 180°, we can conclude that we have found out the correct measure of a .
Therefore, the measure of the unknown angle a = 50°
\texttt{\color{olive}Solution (d) :}Solution (d) :
Measure of the first angle = 90°
Measure of the second angle = x
Measure of the third angle = x
The sum of all three of these angles = 180°(angle sum property)
Which means :-
=\texttt{90 + \: } x \texttt{ \: + \: } x \texttt{ \: = 180}=90 + x + x = 180
= \texttt{90 + 2}x \texttt{ \: = 180}=90 + 2x = 180
= \texttt{2}x \texttt{ \: = 180 - 90}=2x = 180 - 90
=\texttt{2}x \texttt{ \: = \: 90}°=2x = 90°
= x\texttt{ \: = \: } \frac{\texttt{90}}{\texttt{2}}=x =
2
90
=\color{hotpink} ∠x\texttt{ = 45}°=∠x = 45°
Now let us check whether or not we have found out the correct measure of x by placing 45 in the place of x :-
= \texttt{90 + 45 + 45 = 180}=90 + 45 + 45 = 180
=\texttt{180 = 180}=180 = 180
As the measure of the unknown angle we have found out and the other interior angles of this triangle is adding up to 180°, we can conclude that we have found out the correct measure of x .
Therefore, the measure of the unknown angle x = 45°
\texttt{\color{olive}Solution (e) :}Solution (e) :
Measure of the first angle = 40°
Measure of the second angle = 40°
Measure of the third angle = b
The sum of all three of these angles = 180°
Which means :-
=\texttt{40 + 40 + b = 180}=40 + 40 + b = 180
= \texttt{80 + b = 180}=80 + b = 180
=\texttt{b = 180 - 80}=b = 180 - 80
= \color{hotpink}\texttt{∠b = 100}°=∠b = 100°
Now let us check whether or not we have found out the correct measure of b by placing 100 in the place of b :-
=\texttt{ 100 + 40 + 40 = 180}= 100 + 40 + 40 = 180
=\texttt{180 = 180}=180 = 180
As the measure of the unknown angle we have found out and the other interior angles of this triangle is adding up to 180°, we can conclude that we have found out the correct value of b .
Therefore, the measure of the unknown angle b = 100°