Question

question 7 (1 point) find m∠bdc (-3x + 20)° (-2x + 55)° d a a 75° b 25° c 29° d 61° question 8 (1 point) tell whether ∠1 and ∠2 are only adjacent, adjacent and form a linear pair, or not adjacent. a not adjacent b adjacent and form a linear pair c only adjacent

Explanation:

Question 7

Step1: Set up equation

Since the sum of the two angles at point $D$ is $90^{\circ}$ (right - angle), we have $(-3x + 20)+(-2x + 55)=90$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms, we get $(-3x-2x)+(20 + 55)=90$, which simplifies to $-5x+75 = 90$.

Step3: Solve for $x$

Subtract 75 from both sides: $-5x=90 - 75$, so $-5x=15$. Then divide both sides by - 5, and we find $x=-3$.

Step4: Find $m\angle BDC$

Substitute $x = - 3$ into the expression for $\angle BDC$ which is $-3x + 20$. So $m\angle BDC=-3\times(-3)+20=9 + 20=29^{\circ}$.

Adjacent angles have a common side and a common vertex. A linear - pair of adjacent angles form a straight line (sum to $180^{\circ}$). $\angle1$ and $\angle2$ have a common side $\overline{BA}$ and a common vertex $A$. They do not form a straight line.

Answer:

c. $29^{\circ}$

Question 8