Question
From the following figure find ;$(i)\ x\ (ii) \ \angle ABC\ (iii)\ \angle \ ACD$
✓
Answer
$(i)$ In Quadrilateral $ABCD$,
$x+4 x+3 x+4 x+48^{\circ}=360^{\circ}$
$ 12 x=360^{\circ}-48^{\circ}$
$ 12 x=312$
$ x=\frac{312}{12}=26^{\circ}$
$(ii) \angle \mathrm{ABC}=4 \mathrm{x}$
$4 \times 26=104^{\circ}$
$(iii) \angle \mathrm{ACD}=180^{\circ}-4 \mathrm{x}-48^{\circ}$
$=180^{\circ}-4 \times 26^{\circ}-48^{\circ}$
$=180^{\circ}-104^{\circ}-48^{\circ}$
$ =180^{\circ}-152^{\circ}=28^{\circ}$
$x+4 x+3 x+4 x+48^{\circ}=360^{\circ}$
$ 12 x=360^{\circ}-48^{\circ}$
$ 12 x=312$
$ x=\frac{312}{12}=26^{\circ}$
$(ii) \angle \mathrm{ABC}=4 \mathrm{x}$
$4 \times 26=104^{\circ}$
$(iii) \angle \mathrm{ACD}=180^{\circ}-4 \mathrm{x}-48^{\circ}$
$=180^{\circ}-4 \times 26^{\circ}-48^{\circ}$
$=180^{\circ}-104^{\circ}-48^{\circ}$
$ =180^{\circ}-152^{\circ}=28^{\circ}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
By which least number should the given number be divided to obtain a perfect square number and also, find the resulting perfect square number and its square root :
4500
4500
Evaluate: $(9 − y) (7 + y)$
→Divide $Rs. 15,600$ into two parts such that the interest on one at $5$ percent for $5$ years may be equal to that on the other at $4 \frac{1}{2}$ percent for $6$ years.
→$5\%$ pupil in a town died due to some diseases and $3\%$ of the remaining left the town. If $2, 76, 450$ pupil are still in the town; find the original number of pupil in the town.
→A man spends $87\%$ of his salary. If he saves $Rs.325$; find his salary.
→Use the direct method to evaluate : $(2+a) (2−a)$
→The area of a rhombus is equal to the area of a triangle. If the base $ \triangle$ is $24 \ cm$, its corresponding altitude is $16 \ cm$ and one of the diagonals of the rhombus is $19.2 \ cm$. Find its other diagonal.
→Given the universal set $=\{x : x \in N$ and $x < 20\}$, find: $B = \{y : y = 2n + 3, n \in N\}$
→If $a + b = 6$ and $ab=8,$ find $: a^3 + b^3.$
→There are 900 creatures in a zoo as per list given below :
Represent the above data by a pie-chart.
| Beast animals | Other land animals | Birds | Water animals | Reptiles |
| 120 | 400 | 170 | 135 | 75 |