Question

1. what is the measure of ∠bcd? a 35° b 55° c 90° d 125°

Explanation:

Step1: Recall angle - sum property of a triangle

In $\triangle ABC$, the sum of interior angles is $180^{\circ}$. Given $\angle A = 35^{\circ}$ and $\angle B=90^{\circ}$. Let $\angle ACB=x$. Then $\angle A+\angle B + x=180^{\circ}$.

Step2: Calculate $\angle ACB$

Substitute the known values into the angle - sum formula: $35^{\circ}+90^{\circ}+x = 180^{\circ}$. So, $x=180^{\circ}-(35^{\circ}+90^{\circ})=55^{\circ}$.

Step3: Use linear - pair property

$\angle BCD$ and $\angle ACB$ form a linear pair. A linear pair of angles is supplementary, i.e., $\angle BCD+\angle ACB = 180^{\circ}$. Since $\angle ACB = 55^{\circ}$, then $\angle BCD=180^{\circ}-\angle ACB$.

Step4: Calculate $\angle BCD$

$\angle BCD=180^{\circ}- 55^{\circ}=125^{\circ}$.

Answer:

[d] $125^{\circ}$