Question

(1) 34 + 88 = 180
122 = - 122
58
(2) 45 + 90 = 180
=-
(3) 10 + 102 = 180
=-
(4) x + 50 = 180

• 50 - 50

x = 130 ÷ 2
x =
(5)
24 + 106 =
x =
(6)
70 + 32 =
x =

Explanation:

Step1: Solve \(34 + 88-180\)

First, calculate \(34+88 = 122\). Then \(122-180=-58\).

Step2: Solve \(45 + 90-180\)

Calculate \(45 + 90=135\). Then \(135-180=-45\).

Step3: Solve \(10+102 - 180\)

Calculate \(10 + 102=112\). Then \(112-180=-68\).

Step4: Solve \(x + 50=180\)

Subtract 50 from both sides: \(x=180 - 50=130\).

Step5: Solve for \(x\) in the triangle with angles \(24^{\circ}\) and \(106^{\circ}\)

Using the triangle - angle sum formula (\(x+24 + 106=180\)). First, \(24+106 = 130\). Then \(x=180-(24 + 106)=50\).

Step6: Solve for \(x\) in the triangle with angles \(32^{\circ}\) and \(70^{\circ}\)

Using the triangle - angle sum formula (\(x+32 + 70=180\)). First, \(32+70 = 102\). Then \(x=180-(32 + 70)=48\).

Answer:

(1) \(-58\); (2) \(-45\); (3) \(-68\); (4) \(x = 130\); (5) \(x = 50\); (6) \(x = 48\)