In Fig. 6.30, if $ \mathrm{AB} \| \mathrm{CD} $, EF $ \perp \mathrm{CD} $ and $ \angle \mathrm{GED}=126^{\circ} $, find $ \angle \mathrm{AGE}, \angle \mathrm{GEF} $ and $ \angle \mathrm{FGE} $.
"
Given :
$AB \parallel CD$ and $EF$ is perpendicular to $CD$.
$\angle GED = 120^o$.
To find :
We have to find $\angle GEC, \angle EGF, \angle GEF$
Solution :
$\angle GEF + \angle CEG = 120^o$
$120^o = \angle GEF + 90^o$
$\angle GEF = 120^o-90^o$
$\angle GEF = 30^o$
$CD$ is a straight line.
Therefore,
$\angle GED + \angle CEG = 180^o$
$120^o+\angle CEG = 180^o$
$\angle CEG = 180^o-120^o$
$\angle GEC = 60^o$
In Triangle $GFE$,
$\angle GFE + \angle GEF+ \angle EGF= 180^o$
$90^o+30^o+\angle EGF= 180^o$
$\angle EGF= 180^o-120^o$
$\angle EGF= 60^o$.
$\angle GEF = 30^o$ , $\angle GEC = 60^o$
$\angle EGF= 60^o$.
- Related Articles
- In Fig. 6.13, lines \( \mathrm{AB} \) and \( \mathrm{CD} \) intersect at \( \mathrm{O} \). If \( \angle \mathrm{AOC}+\angle \mathrm{BOE}=70^{\circ} \) and \( \angle \mathrm{BOD}=40^{\circ} \), find \( \angle \mathrm{BOE} \) and reflex \( \angle \mathrm{COE} \)."\n
- In Fig. 6.32, if \( \mathrm{AB} \| \mathrm{CD}, \angle \mathrm{APQ}=50^{\circ} \) and \( \angle \mathrm{PRD}=127^{\circ} \), find \( x \) and \( y \)."\n
- In Fig. 6.41, if \( \mathrm{AB} \| \mathrm{DE}, \angle \mathrm{BAC}=35^{\circ} \) and \( \angle \mathrm{CDE}=53^{\circ} \), find \( \angle \mathrm{DCE} \)."\n
- In Fig. \( 6.40, \angle \mathrm{X}=62^{\circ}, \angle \mathrm{XYZ}=54^{\circ} \). If \( \mathrm{YO} \) and \( Z \mathrm{O} \) are the bisectors of \( \angle \mathrm{XYZ} \) and \( \angle \mathrm{XZY} \) respectively of \( \triangle \mathrm{XYZ} \) find \( \angle \mathrm{OZY} \) and \( \angle \mathrm{YOZ} \)."\n
- Find \( \mathrm{x} \) if \( \mathrm{AB}\|\mathrm{CD}\| \mathrm{EF} \)."\n
- In Fig. 6.42, if lines \( \mathrm{PQ} \) and \( \mathrm{RS} \) intersect at point \( \mathrm{T} \), such that \( \angle \mathrm{PRT}=40^{\circ}, \angle \mathrm{RPT}=95^{\circ} \) and \( \angle \mathrm{TSQ}=75^{\circ} \), find \( \angle \mathrm{SQT} \)."\n
- In Fig. 6.29, if \( \mathrm{AB}\|\mathrm{CD}, \mathrm{CD}\| \mathrm{EF} \) and \( y: z=3: 7 \), find \( x \)."\n
- In Fig. 7.21, \( \mathrm{AC}=\mathrm{AE}, \mathrm{AB}=\mathrm{AD} \) and \( \angle \mathrm{BAD}=\angle \mathrm{EAC} \). Show that \( \mathrm{BC}=\mathrm{DE} \)."\n
- In Fig. 6.43, if \( \mathrm{PQ} \perp \mathrm{PS}, \mathrm{PQ} \| \mathrm{SR}, \angle \mathrm{SQR}=28^{\circ} \) and \( \angle \mathrm{QRT}=65^{\circ} \), then find the values of \( x \) and \( y \)."\n
- In Fig. 6.15, \( \angle \mathrm{PQR}=\angle \mathrm{PRQ} \), then prove that \( \angle \mathrm{PQS}=\angle \mathrm{PRT} \)"\n
- \( \mathrm{AB} \) and \( \mathrm{CD} \) are respectively the smallest and longest sides of a quadrilateral \( \mathrm{ABCD} \) (see Fig. 7.50). Show that \( \angle A>\angle C \) and \( \angle \mathrm{B}>\angle \mathrm{D} \)."\n
- \( \mathrm{ABC} \) is a right angled triangle in which \( \angle \mathrm{A}=90^{\circ} \) and \( \mathrm{AB}=\mathrm{AC} \). Find \( \angle \mathrm{B} \) and \( \angle \mathrm{C} \).
- In figure, if \( \angle \mathrm{A}=\angle \mathrm{C}, \mathrm{AB}=6 \mathrm{~cm}, \mathrm{BP}=15 \mathrm{~cm} \), \( \mathrm{AP}=12 \mathrm{~cm} \) and \( \mathrm{CP}=4 \mathrm{~cm} \), then find the lengths of \( \mathrm{PD} \) and CD."
- In the figure two straight lines \( \mathrm{AB} \& \mathrm{CD} \) intersect at \( \mathrm{O} \). If \( \angle \mathrm{COT}=60^{\circ} \), find \( \mathrm{a}, \mathrm{b}, \mathrm{c} \)."\n
- \( \triangle \mathrm{ABC} \sim \triangle \mathrm{QPR} . \) If \( \angle \mathrm{A}+\angle \mathrm{B}=130^{\circ} \) and \( \angle B+\angle C=125^{\circ} \), find \( \angle Q \).
Kickstart Your Career
Get certified by completing the course
Get Started