Sasha sketches a proof of the theorem that vertical angles are congruent. she uses the diagram below. image 60e77c675d4148c2bd12b955d853b377 angle 1 is supplementary to angle 2. angle 3 is supplementary to angle 2. by the transitive property of equality, the measure of angle 1 is equal to the measure of angle 3. angles 1 and 3 are congruent. all vertical angles are congruent. which expression represents the measure of both angle 1 and angle 3? a 2⋅m∠2 b 90°+m∠2 c 180°−m∠1 d 180°−m∠2

Option D (180°-m∠2)

Step-by-step explanation:

we know that

m∠1+m∠2=180° > equation A (by supplementary angles)

m∠3+m∠2=180° > equation B (by supplementary angles)

m∠1=m∠3 > equation C (by vertical angles)

Solve for m∠1 in equation A

m∠1=180°-m∠2

Remember that

m∠1=m∠3

so

m∠3=180°-m∠2

therefore

m∠1=180°-m∠2

m∠3=180°-m∠2

The expression that represent the measure of both angle 1 and angle 3 is

(180°-m∠2)

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°