Mathematics

# State true or false:The bisectors of two adjacent supplementary angles include a right angle.

True

##### SOLUTION
$We\quad know\quad -\\ Two\quad angles\quad whose\quad sum\quad is\quad { 180 }^{ o }\quad are\quad said\quad to\quad be\quad supplementary.\\ A\quad line\quad which\quad divides\quad any\quad angle\quad into\quad equal\quad parts\quad is\quad called\quad as\quad the\quad bisector\quad of\quad that\quad angle.\\ From\quad the\quad figure,\quad \angle ACD\quad \& \quad \angle DCB\quad are\quad two\quad adjacent\quad angles\quad which\quad are\quad supplementary.\\ \angle ACD+\angle DCB={ 180 }^{ o }\quad \qquad ----\left( 1 \right) \\ Let\quad EC\quad \& \quad CF\quad be\quad the\quad angle\quad bisectors\quad of\quad \angle ACD\quad \& \quad \angle DCB\quad respectively.\\ So\quad \angle AEC=\angle ECD\quad \& \quad \angle AEC+\angle ECD=\angle ACD\Rightarrow 2\angle ECD=\angle ACD\quad \quad ----\left( 2 \right) \qquad \\ Also\quad \angle DCF=\angle FCB\quad \& \quad \angle DCF+\angle FCB=\angle DCB\Rightarrow 2\angle DCF=\angle DCB\quad ----\left( 3 \right) \\ Using\quad \left( 2 \right) \quad \& \quad \left( 3 \right) \quad in\quad \left( 1 \right) \\ 2\angle ECD+2\angle DCF={ 180 }^{ o }\Rightarrow 2\left( \angle ECD+\angle DCF \right) ={ 180 }^{ o }\Rightarrow \angle ECD+\angle DCF=\frac { { 180 }^{ o } }{ 2 } \Rightarrow \angle ECD+\angle DCF={ 90 }^{ o }\Rightarrow \angle ECF={ 90 }^{ o }\quad \left[ From\quad figure \right] \\ Here\quad \angle ECF\quad is\quad the\quad angle\quad included\quad by\quad the\quad angle\quad bisectors.\\ Hence\quad the\quad bisectors\quad of\quad two\quad adjacent\quad supplementary\quad angles\quad always\quad include\quad a\quad right\quad angle.$

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

TRUE/FALSE Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
In the given figure of $\triangle ABC$, let $\angle A=50^{o}, B=60^{o},$ and $C=70^{o}$. If mid-point of side $AB, BC$ and $CA$ are $D, E$ and $F$ respectively then find $\angle DEF$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
In given figure find $x$
• A. $120^{0}$
• B. $130^{0}$
• C. $140^{0}$
• D. $110^{0}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
Identify the following pairs of angles as complementary, supplementary or equal.

• A. $177^{\circ}$ and $177^{\circ}$
• B. $7^{\circ}$ and $173^{\circ}$
• C. $3^{\circ}$ and $87^{\circ}$
• D. $45^{\circ}$ and $45^{\circ}$
• E. $90^{\circ}$ and $90^{\circ}$
• F. $77^{\circ}$ and $103^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
Write the supplement of:

$(x+35)^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
The sum of two vertically opposite angles is $166^o$. Find each of the angles.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020