Question

find the measure of the angle indicated.

1. find ( mangle s ).
2. find ( mangle h ).
3. find ( mangle fab ).
4. find ( mangle ydc ).

Explanation:

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15) Find $m\angle S$

Step1: Use exterior angle theorem

The exterior angle $\angle JR T = 140^\circ$ equals the sum of the two remote interior angles $\angle S$ and $\angle T$.
$$140 = (3x+4) + (8x+4)$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$140 = 11x + 8$$
$$11x = 140 - 8 = 132$$
$$x = \frac{132}{11} = 12$$

Step3: Calculate $m\angle S$

Substitute $x=12$ into $3x+4$.
$$m\angle S = 3(12)+4 = 36+4 = 40$$

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16) Find $m\angle H$

Step1: Use exterior angle theorem

The exterior angle $\angle DFG = 14x+1$ equals the sum of $\angle G$ and $\angle H$.
$$14x+1 = 89 + (5x-7)$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$14x+1 = 5x + 82$$
$$14x - 5x = 82 - 1$$
$$9x = 81$$
$$x = \frac{81}{9} = 9$$

Step3: Calculate $m\angle H$

Substitute $x=9$ into $5x-7$.
$$m\angle H = 5(9)-7 = 45-7 = 38$$

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17) Find $m\angle FAB$

Step1: Use exterior angle theorem

The exterior angle $\angle FCA = 13x-3$ equals the sum of $\angle B$ and $\angle BAC$.
$$13x-3 = (3x+2) + 55$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$13x-3 = 3x + 57$$
$$13x - 3x = 57 + 3$$
$$10x = 60$$
$$x = \frac{60}{10} = 6$$

Step3: Calculate $m\angle FAB$

Substitute $x=6$ into $13x-3$.
$$m\angle FAB = 13(6)-3 = 78-3 = 75$$

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18) Find $m\angle YDC$

Step1: Use exterior angle theorem

The exterior angle $\angle YDC = 15x+5$ equals the sum of $\angle C$ and $\angle B$.
$$15x+5 = 80 + (6x+6)$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$15x+5 = 6x + 86$$
$$15x - 6x = 86 - 5$$
$$9x = 81$$
$$x = \frac{81}{9} = 9$$

Step3: Calculate $m\angle YDC$

Substitute $x=9$ into $15x+5$.
$$m\angle YDC = 15(9)+5 = 135+5 = 140$$

Answer:

1. $m\angle S = 40^\circ$
2. $m\angle H = 38^\circ$
3. $m\angle FAB = 75^\circ$
4. $m\angle YDC = 140^\circ$