Question

In a quadrilateral ABCD, angle C=64, angle d = angle c -8, angle a = 5(a+2) and angle b = 2 (2a+7). Calculate angle a

Answer 1

angle a = 5( a+2)
angle b = 2(2a+7)
angel c = 64
angle d = angle c - 8
= 64°-8 ( angle c = 64)
= 56°
We know that,
sum of all angles of a quadrilateral = 360°
Now,
angle a + angle b + angle c + angle d = 360°
5( a+2)° + 2(2a+7)° + 64° + 56° = 360°
5a + 10°+ 4a + 14° + 64° + 56°=360°
5a + 4a + 10° + 14° + 120° =360°
9a + 24° + 120° = 360°
9a + 144° = 360°
9a = 360°- 144°
9a = 216°
a = 216/9
a = 24°
Now,
angle a = 5(a+2)
= 5(24+2)
= 5(26)
= 130°
angle b = 2(2a+7)
= 2[2(24)+7]
= 2[48+7]
= 2(55)
= 110°