Question

geometry - notes 2 - 1 part 1 practice name__ date period__ show all your work to answer each question. 1. if m∠fgb = 105° and m∠bgh = 94°, find m∠fgh. 2. if m∠aik = 61° and m∠ijk = 153°, find ∠uia. 3. if m∠vut = 175°, m∠vui=(17x - 3)°, and m∠jut=(17x + 8)°. find x. 4. if ∠abc=(17x + 8)°, m∠abk = 42° and m∠kbc=(12x - 4)°. find m∠abc.

Explanation:

Step1: Recall angle - addition postulate

The measure of an angle formed by two non - overlapping angles with a common ray is the sum of the measures of the two angles.

Step2: Solve for $\angle FGH$ in question 1

We know that $\angle FGB+\angle BGH = \angle FGH$. Given $\angle FGB = 105^{\circ}$ and $\angle BGH=54^{\circ}$, then $\angle FGH=105^{\circ}+ 54^{\circ}=159^{\circ}$.

Step3: Solve for $\angle UJA$ in question 2

We know that $\angle UJK=\angle UJA+\angle AJK$. So, $\angle UJA=\angle UJK - \angle AJK$. Given $\angle AJK = 61^{\circ}$ and $\angle UJK = 153^{\circ}$, then $\angle UJA=153^{\circ}-61^{\circ}=92^{\circ}$.

Step4: Solve for $x$ in question 3

Since $\angle VUT=\angle VUJ+\angle JUT$, we substitute the given expressions: $175=(17x - 3)+(17x + 8)$.
First, combine like - terms: $175=17x-3 + 17x+8=34x + 5$.
Then, subtract 5 from both sides: $175 - 5=34x$, so $170 = 34x$.
Divide both sides by 34: $x = 5$.

Step5: Solve for $\angle ABC$ in question 4

Since $\angle ABC=\angle ABK+\angle KBC$, we substitute the given expressions: $17x + 8=42+(12x - 4)$.
First, simplify the right - hand side: $17x + 8=12x+38$.
Subtract $12x$ from both sides: $17x-12x + 8=12x-12x + 38$, so $5x+8 = 38$.
Subtract 8 from both sides: $5x=30$.
Divide both sides by 5: $x = 6$.
Then find $\angle ABC$ by substituting $x = 6$ into the expression for $\angle ABC$: $\angle ABC=17\times6+8=102 + 8=110^{\circ}$.

Answer:

1. $m\angle FGH = 159^{\circ}$
2. $m\angle UJA=92^{\circ}$
3. $x = 5$
4. $m\angle ABC = 110^{\circ}$