Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a… - Vidyadip

Question

Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.

✓

Answer

∵ ∠C = 64° (Given)
∴ ∠D = ∠C – 8° = 64°- 8° = 56°
∠A = 5(a+2)°
∠B = 2(2a+7)°
Now ∠A + ∠B + ∠C + ∠D = 360°
5(a+2)° + 2(2a+7)° + 64° + 56° = 360°
5a + 10 + 4a + 14° + 64° + 56° = 360°
9a + 144° = 360°
9a = 360° – 144°
9a = 216°
a = 24°
∴ ∠A = 5 (a + 2) = 5(24+2) = 130°

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Quadrilateral→Quadrilateral — all question types→MATHS STD 6 question papers→ICSE Board STD 6 question papers→ICSE Board question paper generator→

Similar questions

Find the L.C.M. of the following, use common division method : 16, 18, 24, 32, 36

Solve : $y-3 \frac{1}{2}=2 \frac{1}{3}$

By weight, $90\%$ of tomato and $78\%$ of potato is water. Find the weight of water in $25\ kg$ of tomato.

Each side of a square tile is $60 \ cm$. How many tiles will be required to cover the floor of a hall with length $= 50 \ m$ and breadth $= 36\ m$.

A distance of $14.4$ km is covered in $2$ hours $40$ minutes. Find the speed in $ms^{−1}$. With this speed Sakshi goes to her school, $240\ m$ away from her house, and then returns back. How much time, in all, will Sakshi take?

A student multiplied 8,035 by 87 instead of multiplying by 78. By how much was his answer greater than or less than the correct answer?

An objective test was given to a group of 168 students. It was found that $\frac{5}{6}$ of the students gave all correct answers. How many students made 1 or more mistakes?

The product of three numbers is $7 \frac{1}{2}$. If two of them are $1 \frac{1}{7}$ and $3 \frac{3}{4}$, find the third number.

Draw a line segment AB = 6 cm. Without using set squares, draw angle OAB = 60° and angle OBA = 90°. Measure angle AOB and write this measurement.

Only one-fifth of water is available in liquid form. This limited amount of water is replenished and used by man recurrently. Express this information as percent, showing:
(i) water available in liquid form.
(ii) water available in frozen form.