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Answer: 78°

Step-by-step explanation:

Looking at the picture, we can tell that ∠ACD and ∠DCB are supplementary angles. This means, they are equal to 180°. With that, we can find x and plug it into ∠DCB.

4x+2+3x+3=180            [combine like terms]

7x+5=180                       [subtract both sides by 5]

7x=175                           [divide both sides by 7]

x=25

Now that we know x=25, we can plug it in to find ∠DCB.

3(25)+3                         [multiply]

75+3                               [add]

78

Now, we know ∠DCB is 78°.

TheAstrophile

[tex] \sf\huge {\dag Question } [/tex]

[tex] \qquad \qquad [/tex] "Diagram"

Determine the value of m∠DCB.

[tex] \sf\huge { \dag Solution } [/tex]

Here, in the diagram it is forming supplementary angle,

[The two angles that gives 180° when they add up are called]

So, we can conclude that,

[tex] \sf { \angle DCA + \angle DCB = 180°} [/tex]

[tex] \sf { 4x + 2 + 3x + 3 = 180°} [/tex] [ Put the values and formed the suitable equation. ]

[tex] \sf { \implies 4x + 3x + 2 + 3 = 180°} [/tex]

[tex] \sf { \implies 7x + 5 = 180°} [/tex]

[tex] \sf { \implies 7x = 180° - 5} [/tex]

[tex] \sf { \implies 7x = 175} [/tex]

[tex] \sf\red { \implies x = \cancel{\dfrac{175}{7}} = 25°} [/tex]

Value of x is 25°.

Now, put the value in the expression 3x + 3 (measurement of m∠DCB)

[tex] \sf { \longrightarrow 3x +3}[/tex]

[tex] \sf { \longrightarrow 3 \times 25 +3}[/tex]

[tex] \sf { \longrightarrow 75 +3}[/tex]

[tex] \sf { \longrightarrow 78}[/tex]

[tex] \therefore [/tex] The value of m∠DCB is 78°.

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