Question

find the measure of angle adc

Answer 1

Ello There!

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Answer

Here we are asked to find ∠ADC.

First, we try to form any equation we can use, to possibly find this angle.

We have an equation based off of linear pair, the exterior angle to it is x + 10°

∴ x + 10 + ∠ADC = 180

But we dont have the value of 'x + 10', therefore, lets obtain the value of it.

Sum of exterior angles of a quadrilateral = 360°

x + 10° + (2x + 2)° + (4x - 24)° + (3x + 2)° = 360°

(Calculating all the variables and numbers)

10x - 10° = 360°

10x = 360° + 10°

10x = 370°

x = $\frac{370}{10}$

x = 37

We now substitute this value in x + 10°

x + 10°

37°  + 10°

47°

Now, we use the equation we penned down at the start

x + 10° + ∠ADC = 180° (Linear Pair)

47 + ∠ADC = 180°

∠ADC = 180° - 47°

∠ADC = 133°

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Answer 2

Answer:

Step-by-step explanation:

x + 10 + ∠ADC = 180

But we dont have the value of 'x + 10', therefore, lets obtain the value of it.

Sum of exterior angles of a quadrilateral = 360°

x + 10° + (2x + 2)° + (4x - 24)° + (3x + 2)° = 360°

10x - 10° = 360°

10x = 360° + 10°

10x = 370°

x = 37

We now substitute this value in x + 10°

x + 10°

37°  + 10°

47°

Now, we use the equation we penned down at the start

x + 10° + ∠ADC = 180° (Linear Pair)

47 + ∠ADC = 180°

∠ADC = 180° - 47°

= 133°