Question

Pl help me to solve this​

Answer 1

Question :

$\sf \small In \: the \: given \: figure : \: \angle b = 2a +15 \degree \: and \: \angle c = 3a + 5 \degree \: find \: b \: and \: c$

Solution :

Sum of interior angles of a quadrilateral = 360°

→ a + b + c + 70° = 360°

By putting the values of b and c we get,

→ a + 2a + 15° + 3a + 5° + 70° = 360°

By adding we get,

→ 6a + 90° = 360°

We have to shift 90° to the LHS of the equation

→ 6a = 360° – 90°

→ 6a = 270°

→ a = 270°/6

→ a = 45°

Now,

By putting the values in both equations of b and c we will get the answer

$\sf \small \angle b = 2a + 15 \degree$

Replacing a with 45° we get

$\sf \small \angle b = 2 \times 45 \degree + 15 \degree$

$\sf \small \angle b = 90 \degree + 15 \degree$

$\sf \small \angle b = 105\degree$

Now in angle c

$\sf \small \angle c = 3a + 5 \degree$

$\sf \small \angle c = 3 \times 45 + 5 \degree$

$\sf \small \angle c = 135 \degree + 5 \degree$

$\sf \small \angle c = 140 \degree$

Final Answer :

$\underline{ \boxed{ \purple{\sf \small \angle b = 105\degree }}}$

$\underline{ \boxed{ \green{\sf \small \angle c = 140\degree }}}$

Verification :

• Sum of interior angles = 360°

• a + b + c + 70° = 360°

• 45° + 105° + 140° + 70° = 360°

• 360° = 360°

Hence,Proved !!

Answer 2

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

• Sum of int. Angles Of A Quadrilateral = 360°

• a + b + c + 70° = 360°
• a + 2a + 15° + 3a + 5° + 70° = 360°
• 6a + 90° = 360°
• 6a = 360° – 90°
• 6a = 270°
• a = 270°/6
• a = 45°

• ∠b = 2a+15°
• ∠b = 2×45°+15°
• ∠b = 90°+15°
• ∠b = 105°

• ∠c = 3a+5°
• ∠c = 3×45+5°
• ∠c = 135°+5°
• ∠c = 140°

Answer 3

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

• Sum of int. Angles Of A Quadrilateral = 360°

• a + b + c + 70° = 360°
• a + 2a + 15° + 3a + 5° + 70° = 360°
• 6a + 90° = 360°
• 6a = 360° – 90°
• 6a = 270°
• a = 270°/6
• a = 45°

• ∠b = 2a+15°
• ∠b = 2×45°+15°
• ∠b = 90°+15°
• ∠b = 105°

• ∠c = 3a+5°
• ∠c = 3×45+5°
• ∠c = 135°+5°
• ∠c = 140°