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(c) $\newline$ (d) $\newline$ (e) $\newline$ (f) $\newline$ $5$ . In the figure, $A B / / D E, G C / / D F, B C D$ is a straight line, $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ and $E \hat{D} F=84^{\circ}$ . $\newline$ Find $\newline$ (i) $C \hat{D} E$ , $\newline$ (ii) $A \hat{B} H$ . $\newline$ D. Find the $\newline$ (c) $\newline$ $7$ . In the figure, $A B / / D F, E C / / G H, F \hat{E H}=26^{\circ}$ and $E \hat{H} G=62^{\circ}$ . $\newline$ (i) $D \hat{E} H$ , $\newline$ (ii) $A \hat{B} C$ . $\newline$ $8$ . In the figure, $A C / / F G, D B / / F E$ , reflex $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $0$ and $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $1$ . $\newline$ Find $\newline$ (i) $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $2$ , $\newline$ (ii) $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $3$ . $\newline$ (ii) $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $4$ . $\newline$ $9$ . In the figure, $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $5$ is a straight line and $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $6$ . Find the value of $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $7$ and of $C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}$ $8$ . $\newline$ (a)

Full solution

Q. (c)

\newline

(d)

\newline

(e)

\newline

(f)

\newline

5

. In the figure,

A B / / D E, G C / / D F, B C D

is a straight line,

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

and

E \hat{D} F=84^{\circ}

\newline

Find

\newline

(i)

C \hat{D} E

\newline

(ii)

A \hat{B} H

\newline

D. Find the

\newline

(c)

\newline

7

. In the figure,

A B / / D F, E C / / G H, F \hat{E H}=26^{\circ}

and

E \hat{H} G=62^{\circ}

\newline

(i)

D \hat{E} H

\newline

(ii)

A \hat{B} C

\newline

8

. In the figure,

A C / / F G, D B / / F E

, reflex

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

0

and

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

1

\newline

Find

\newline

(i)

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

2

\newline

(ii)

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

3

\newline

(ii)

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

4

\newline

9

. In the figure,

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

5

is a straight line and

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

6

. Find the value of

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

7

and of

C \hat{B} H=74^{\circ}, D \hat{C} G=148^{\circ}

8

\newline

(a)

Identify Corresponding Angles: Identify corresponding angles due to parallel lines $AB$ and $DE$ . Since $AB$ is parallel to $DE$ and $GC$ is parallel to $DF$ , angle $\hat{C}BH$ corresponds to angle $\hat{E}DF$ . Calculation: $\hat{C}BH = \hat{E}DF = 74^\circ$ .
Find Angle $C\hat{D}E$ : Find angle $C\hat{D}E$ using the straight line BCD. Angle BCD is a straight line, so angles $C\hat{B}H$ and $D\hat{C}G$ form a straight line and their sum is $180$ degrees. Calculation: $C\hat{D}E = 180 - D\hat{C}G = 180 - 148 = 32$ degrees.
Find Angle $\hat{A}BH$ : Find angle $\hat{A}BH$ using the corresponding angles. $\newline$ Since $AB$ is parallel to $DE$ , angle $\hat{A}BH$ corresponds to angle $\hat{E}DF$ . $\newline$ Calculation: $\hat{A}BH = \hat{E}DF = 84^\circ$ .