Question

DUU - 0 -
30°
7. In the Fig.,
EA || BC and ABC
is a right triangle
drawn in which
B = 90°, BC is ca
base and ZACB = 30°
A line from B is drawn to meet AC at D
so that DB = DC. Find the values of
P,Q,r.​

Answer 1

$\huge\underline\mathfrak{\sf{Correct\:Question-}}$

In the Fig, EA || BC and ABC is a right triangle, in which ∠B = 90°, BC is base and ∠ACB = 30°. A line from B is drawn to meet AC at D, so that DB = DC. Find the values of p, q and r.

$\huge\underline\mathfrak{\sf{Answer-}}$

p = 30°

q = 60°

r = 60°

$\huge\underline\mathfrak{\sf{Explanation-}}$

It is given that, EA || BC,

$\therefore$ ∠EAC = ∠ACB

$\implies$ $\red{\sf{p=30°}}$

Also, it is given that; DB = DC

$\therefore$ ∠ACB = ∠DBC

[ Angles opposite to equal sides are equal ]

$\implies$ ∠DBC = 30° ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Now,

∠B = 90° ( given )

$\implies$ r + ∠DBC = 90°

$\implies$ r + 30° = 90°

$\implies$ r = 90° - 30°

$\implies$ $\red{\sf{r=60°}}$

__________________

In ∆ABC,

∠A + ∠B + ∠C = 180° ( By Angle sum property )

$\implies$ q + 90° + 30° = 180°

$\implies$ q + 120° = 180°

$\implies$ q = 180° - 120°

$\implies$ $\red{\sf{q=60°}}$

Answer 2

$\huge\underline\text{\sf{Correct\:Question:-}}$

In the Fig, EA || BC and ABC is a right triangle, in which ∠B = 90°, BC is base and ∠ACB = 30°. A line from B is drawn to meet AC at D, so that DB = DC. Find the values of p, q and r.

$\huge\underline\text{\sf{Answer:-}}$

★ Given:-

• p = 30°
• q = 60°
• r = 60°

$\huge\underline\mathfrak{\sf{Explanation:-}}$

$\implies$EA || BC.......(Given)

∴ ∠EAC = ∠ACB

$\implies{\sf{p=30°}}$

Also, DB = DC..........(Given)

∴ ∠ACB = ∠DBC

$\implies$∠DBC = 30°⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Now,

$\implies$∠B = 90° ( Given )

$\implies$ r + ∠DBC = 90°

$\implies$ r + 30° = 90°

$\implies$ r = 90° - 30°

$\implies{\sf{r = 60°}}$

________________________________

In ∆ABC,

∠A + ∠B + ∠C = 180° ( By Angle sum property )

$\implies$ q + 90° + 30° = 180°

$\implies$ q + 120° = 180°

$\implies$ q = 180° - 120°

$\implies{\sf{q=60°}}$

__________________________________