Home/Class 9/Maths/

Question and Answer

If one of the angles of a triangle is \( 130°\), then find the angle between the bisectors of the other two angles.

loading
settings
Speed
00:00
02:45
fullscreen

Question

If one of the angles of a triangle is \( 130°\), then find the angle between the bisectors of the other two angles.
Question: If one of the angles of a triangle is  130°, then find the angle between the bisectors of the other two angles.

Answer

We are given that \( \angle\;B=130°\)
Now we know the angle sum property of triangles that the sum of interior angles of a triangle is equal to \( 180°\)
So \( \angle\;A+\angle\;B+\angle\;C=180°\)
Putting the value of \( \angle\;B\) in the above equation, we get,
\( \angle\;A+130°+\angle\;C=180°\)
\( \angle\;A+\angle\;C=180°-130°\)
\( \angle\;A+\angle\;C=50°\)
Now dividing by 2
\( \frac{1}{2}\angle\;A+\frac{1}{2}\angle\;C=25° ...(1)\)
Also, we can apply the sum of angles property in \( ∆ADC\).
Thus, we have,
\( \frac{1}{2}\angle\;A+\frac{1}{2}\angle\;C+\angle\;D=180° ...(2)\)
Now, substituting the value of (1) in equation (2), we get,
\( 25°+\angle\;D=180°\)
\( \angle\;D=180°-25°\)
\( \angle\;D=155° \)
Therefore, the angle between the bisectors of the other two angles is \( 155°\).
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
Correct22
Incorrect0
Watch More Related Solutions
Which of the following has larger bond angle in each pair?\(CO_2, BF_3\)
See the figure and find the following:

(i) The coordinate of the point B
(ii) The coordinate of the point c
(iii) The point identified by  the coordinates? \( \left(-3,-5\right)\)
(iv) point identified by the coordinates \( \left(2,-4\right)\)
(v) The abscissa of the point D
(vi) The ordinate of the point H
(vii) The coordinates of the point L
(viii) The coordinates of the point M
Why oceans do not freeze? Give two reasons.
The unit digit in the square of the number \(27\) is( )
A. \(7\)
B. \(2\)
C. \(5\)
D. \(9\)
Fill in the Blank:
Five kingdom classification of living organisms is given by ___.
Which of the following statements is incorrect?( )
A. Aluminium is a bright silvery-white metal
B. Aluminium forms alloys with \(Cu, Mn, Mg, Si\) and \(Zn\)
C. The use of aluminium and its compounds for domestic purposes is now increased considerably
D. Both (a) and (b)
Which of them has larger bond angle:\(NH_3, CH_4?\)
\(BF_{3}\) easily reacts with Lewis base such as \(NH_3 \) to complete octet around boron. This can be expressed as ( )
A. \(F_{3}B+: NH_{3}\to F_{3}B\leftarrow NH_{3}\)
B. \(F_{3}B+: NH_{3}\to F_{3}B\rightarrow NH_{3}\)
C. \(:BF_3+NH_{3}\to BF_3\rightarrow NH_{3}\)
D. \(:BF_3+NH_{3}\to BF_3\leftarrow NH_{3}\)
Which of the following has larger bond angle?
\(H_{2}O,H_{2}S\) .
Fill in the blank:
Basic smallest unit of classification is___.

Load More