Question

solve this question, along with the steps of construction. ​

Answer 1

$\underline{\underline{\pink{\huge\sf Answer}}}$

1) Draw a line AB = 7 cm

2) Construct a 45° with vertex A and extend it

3) Construct a 60° with vertex B and extend it

4) Mark the point where these two lines Intersect as C

5) Hence ∆ABC has been constructed

━━━━━━━━━━

☯ $\underline{\sf Let's \ understand}$

If you see the Answer we may get a doubt that, we never constructed a 75°. This was because we used the angle sum property ,

Given that in ∆ABC

✭ ∠A = 45°

✭ ∠C = 75°

Angle B will be,

➝ ∠A + ∠B + ∠C = 180°

➝ 45° + ∠B + 75° = 180°

➝ 120° + ∠B = 180°

➝ ∠B = 180°-120°

➝ ∠B = 60°

$\sf\star \ Diagram \ \star$

$\setlength{\unitlength}{1cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(5,5)\qbezier(1,1)(1,1)(8,1)\qbezier(8,1)(8,1)(5,5)\qbezier(1.99,1)(1.9,1.3)(1.7,1.7)\qbezier(7,1)(8,2.3)(7,1)\put(1,0.5){\sf A}\put(7.9,0.5){\sf B}\put(4.9,5.3){\sf C}\end{picture}$

(Also Refer to the attachment)

━━━━━━━━━━━━━━━━

Answer 2

$\sf\orange{ QUESTION :- }$

construct a triangle ABC in which AB = 7 cm , ∠ A = 45° and ∠ C = 75° .

$\sf\blue{ ANSWER :- }$

Given -

✧ ∠A = 45 °

✧ ∠C = 75 °

✧ AB = 7

To Find -

∴∠B = ?

so, first we have to find ∠ B →

∠A + ∠B + ∠C = 180 °

By this we can find ∠B.

[ Angle sum property of triangle states that the sum of interior angles of a triangle is 180°]

↝ ∠A + ∠B + ∠C = 180 °

↝ 45 ° + ∠B + 75 ° = 180 °

↝ 120 ° + ∠B = 180 ° [Adding ∠A & ∠C]

↝ ∠B = 180 ° - 120 ° [By Transposition]

↝ ∠B = 60 ° [Subtracting 180 & ∠A+∠C]

So, now we know that ∠B = 60°

▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬

Let's construct the triangle

1. Draw a line of 7 cm and mark it as AB.

2. Construct ∠A from point A of 45 ° and extend it .

3. then Construct ∠B from point B of 60 ° and extend it.

4. join the both lines at a point C which is ∠C .

[ you can see after measuring ∠C that is it 75° because of Angle sum property (a + b + c = 180 °) ]

5. Now , ∆ ABC has been constructed.

[ Construction is in attachment ] ☺️