Question

∠bca and ∠acd form a linear - pair. ∠bca is represented by (2x - 5)° and ∠acd is represented by (3x + 10)°. what is m∠acd? a. 35° b. 61° c. 85° d. 115°

Explanation:

Step1: Recall linear - pair property

Since $\angle BCA$ and $\angle ACD$ form a linear pair, $\angle BCA+\angle ACD = 180^{\circ}$. So, $(2x - 5)+(3x+10)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+3x - 5 + 10=180$, which simplifies to $5x+5 = 180$.

Step3: Solve for $x$

Subtract 5 from both sides: $5x=180 - 5=175$. Then divide both sides by 5, so $x=\frac{175}{5}=35$.

Step4: Find the measure of $\angle ACD$

Substitute $x = 35$ into the expression for $\angle ACD$: $\angle ACD=3x + 10$. So, $\angle ACD=3\times35+10=105 + 10=115^{\circ}$.

Answer:

D. $115^{\circ}$