a. $$ m(\angle A)=35^{\circ} $$ Identify the measure of a complementary angle of $$ m(\angle A)=35^{\circ} $$. The measure of the complement is $$ \square^{\circ} $$. (Simplify your answer.) Identify the measure of a supplementary angle of $$ m(\angle A)=35^{\circ} $$. The measure of the supplement is $$ \square^{\circ} $$. (Simplify your answer.) Identify the measure of a vertical angle of $$ m(\angle A)=35^{\circ} $$. The measure of the vertical angle of $$ m(\angle A) $$ is $$ \square^{\circ} $$. (Simplify your answer.) b. $$ m(\angle B)=z^{\circ} $$ Identify the measure of a complementary angle of $$ m(\angle B)=z^{\circ} $$. The measure of the complement is $$ \square^{\circ} $$.

Question

UpStudy AI · Accepted Answer

**a. Given $$ m(\angle A) = 35^{\circ} $$:**

1. **Complementary angle:**  
   By definition, complementary angles add to $$ 90^{\circ} $$. Therefore, the measure of the complementary angle to $$ \angle A $$ is  
   $$
   90^{\circ} - 35^{\circ} = 55^{\circ}.
   $$  
   The measure of the complement is $$ 55^{\circ} $$.

2. **Supplementary angle:**  
   By definition, supplementary angles add to $$ 180^{\circ} $$. Hence, the measure of the supplementary angle to $$ \angle A $$ is  
   $$
   180^{\circ} - 35^{\circ} = 145^{\circ}.
   $$  
   The measure of the supplement is $$ 145^{\circ} $$.

3. **Vertical angle:**  
   Vertical angles are equal in measure. Thus, the vertical angle corresponding to $$ \angle A $$ has the same measure:  
   $$
   35^{\circ}.
   $$  
   The measure of the vertical angle of $$ \angle A $$ is $$ 35^{\circ} $$.

---

**b. Given $$ m(\angle B) = z^{\circ} $$:**

1. **Complementary angle:**  
   The complement of $$ \angle B $$ is determined by subtracting its measure from $$ 90^{\circ} $$:
   $$
   90^{\circ} - z^{\circ}.
   $$  
   The measure of the complement is $$ 90^{\circ} - z^{\circ} $$.
**a. Given $$ m(\angle A) = 35^{\circ} $$:** 1. **Complementary angle:** The measure of the complement is $$ 55^{\circ} $$. 2. **Supplementary angle:** The measure of the supplement is $$ 145^{\circ} $$. 3. **Vertical angle:** The measure of the vertical angle is $$ 35^{\circ} $$. --- **b. Given $$ m(\angle B) = z^{\circ} $$:** 1. **Complementary angle:** The measure of the complement is $$ 90^{\circ} - z^{\circ} $$.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions