in figure if AB||CD, CD||EF and y:z= 3:7, find x.
Answers
- AB CD and CD EF
- The ratio of y and z is 3:7.
- The unknown x = ?
We know that,
- Corresponding angles are equal
HERE,
y and z are equal to 180° (linear pair).
So,
- Let's assume that y and z is 3x and 7x.
According to the question,
HENCE,
y = 3x = 3 × 18 =54°
z = 7x = 7 × 18 = 126°
NOW,
We also know that
- Adjacent angles are equal to 180°
THEREAFTER,
we can write it that :
x and y = 180° ( Adjacent angles are equal to 180°).
Substituting the value of y :
FINALLY,
- The unknown
ADDITIONAL THEOREM :
- Adjacent angles are equal to 180°
- Corresponding angles are always equal.
- Opposite vertical angles are always equal.
NOTE :
READ IT CAREFULLY.
Given:
AB\bf \parallel∥ CD and CD\bf \parallel∥ EF
The ratio of \bf \angle∠ y and \bf \angle∠ z is 3:7.
\sf \underline {\orange {To \: find : }}
Tofind:
The unknown \bf \angle∠ x = ?
\sf \underline {\orange {\: Solution : }}
Solution:
We know that,
Corresponding angles are equal
HERE,
\bf \angle∠ y and \bf \angle∠ z are equal to 180° (linear pair).
So,
Let's assume that \bf \angle∠ y and \bf \angle∠ z is 3x and 7x.
According to the question,
\begin{gathered}\orange \leadsto \bf \: \: 3x \: + \: 7x = 180 \degree \: \\ \bf \implies \: 10x \: = 180 \: \degree \\ \bf \implies \:x \: = \frac{18 \cancel0}{1 \cancel0} \\ \bf \red \dag {\underline{ \boxed{ \bf x \: = \: 18 \: \degree}}{\red \dag }}\end{gathered}
⇝3x+7x=180°
⟹10x=180°
⟹x=
1
0
18
0
†
x=18°
†
HENCE,
\bf \angle∠ y = 3x = 3 × 18 =54°
\bf \angle∠ z = 7x = 7 × 18 = 126°
NOW,
We also know that
Adjacent angles are equal to 180°
THEREAFTER,
we can write it that :
\bf \angle∠ x and \bf \angle∠ y = 180° ( Adjacent angles are equal to 180°).
Substituting the value of \bf \angle∠ y :
\begin{gathered}\red \leadsto \bf\angle x \: + \: \angle \: y = 180° \\ \red \leadsto \bf \angle x \: + 54 \degree = 180\degree \\ \bf \red \leadsto \: \angle x = (180 - 54)\degree \\ \bf \red \dag{ \underline{ \boxed{\bf \therefore \: \angle x = 126\degree}}} \red \dag\end{gathered}
⇝∠x+∠y=180°
⇝∠x+54°=180°
⇝∠x=(180−54)°
†
∴∠x=126°
†
FINALLY,
The unknown \bf \therefore \: \angle x = 126\degree∴∠x=126°
ADDITIONAL THEOREM :
Adjacent angles are equal to 180°
Corresponding angles are always equal.
Opposite vertical angles are always equal.