Question

<1 and <2 form a linear pair. If m<1 = (5x + 9)° and m<2 = (3x + 11), find the measure of
each angle.​

Answer 1

Answer :-

$\large\boxed{\red{\bf \blue{\bigstar}\:\: First\:Angle=109^{\circ}}}$

$\large\boxed{\red{\bf \blue{\bigstar}\:\: Second\:Angle=71^{\circ}}}$

Step - by - step Explanation :-

Given :-

• Measure of ∠1 is (5x + 9)°.
• Measure of ∠2 is (3x + 11)° .
• ∠1 and ∠2 are linear pair .

To Find :

• The value of each angle .

Figure :

$\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\put(0,0){\line(1,0){6}}\put(1,0){\vector(-1,0){1}}\put(5,0){\vector(1,0){1}}\put(3,0){\vector(-1,3){1.2}}\put(0,-0.3){ \sf A }\put(3,-0.3){ \sf O }\put(6,-0.2){ \sf B }\put(2.2,3.2){ \sf C }\put(0.4,0.2){\line(0,-1){0.4}}\put(5.6,0.2){\line(0,-1){0.4}}\qbezier(2.5,0)(2.9,1)(2.8,0.5)\qbezier(4,0)(4,1)(2.65,0.9)\put(3.5,1){ \sf 109^{\circ} }\put(3.5,1){ \sf 109^{\circ} }\put(2.2,0.5){ \sf 71^{\circ} }\put(2.2,0.5){ \sf 71^{\circ} }\end{picture}$

Solution :

Since ∠1 and ∠2 are linear pair , so their sum will be 180° .

⇒ ∠1 + ∠2 = 180° .

⇒ (5x + 9)° + (3x + 11)° = 180°.

⇒ 8x + 20° = 180°.

⇒ 8x = 180°-20°.

⇒ 8x = 160°.

⇒ x = 160°/8.

⇒ x = 20° .

Hence the value of x is 20°.

So , the two angles will be ,

• First angle = 5x+9°=100°+9°=109°.
• Second angle=3x+11°=60°+11°=71°.

Answer 2

Step-by-step explanation:

m(∠1) = (5x + 9)° and m(∠2) = (3x + 11)°

Since the angles form a linear pair, the sum of their measures is 180°.

So, (5x + 9) + (3x + 11) = 180

8x + 20 = 180

8x = 160

x = 20°

So, m(∠1) = 109° and m(∠2) = 71°.