Question

I WILL GIVE BRAINLY AS USUAL:Given that measure of angle 6 is 1/8 of measure of angle 4. Find the measures of these two angles if a∥b . Fill in the blanks
I WILL GIVE BRAINLY AS USUAL
Statement Reason

1. a∥b Given

2. m∠6= 1 8 m∠______ Given

3. m∠6+m∠4 =________ __________________________

4. m∠6+8m∠_______ = 180° Substitution

6. m∠6 =____, m∠4=_____ Algebra

Answer 1

∠4 = 160°, ∠6 = 20°

Explanation:

Given that measure of angle 6 is 1/8 of measure of angle 4. Find the measures of these two angles if a∥b .

• 1. a∥b Given
• 2. m∠6= 1 8 m∠______ Given
• 3. m∠6+m∠4 =________ __________________________
• 4. m∠6+8m∠_______ = 180° Substitution
• 6. m∠6 =____, m∠4=_____ Algebra

An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle

There are two angles that can form such as

Supplementary Angles: if both angles are added = 180 ° . Notice that together they make a straight angle, but the angles itself are don't have to be together. For example these two angles 40° and 140° are Supplementary Angles, because they add up to 180 °

Complementary Angles: if both angles are added = 90°. Two angles are Complementary when they are add up to 90 degrees (a Right Angle). For example these two angles (40° and 50°) are Complementary Angles, because they add up to 90°

According to the attached figure, ∠6 and ∠4 are Supplementary Angles

$x + \frac{1}{8} = 180°\\8x + x = 1440°\\x = 160°$

Therefore,

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Answer 2

Answer:

m∠4=160°

m∠6=20°

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

m∠6+m∠4=180° ----> equation A (by consecutive interior angles)

m∠6=(1/8)m∠4 ---> equation B

substitute equation B in equation A

(1/8)m∠4+m∠4=180°

Solve for m∠4

(9/8)m∠4=180°

m∠4=180°(8)/9

m∠4=160°

Find the measure of m∠6

m∠6=(1/8)m∠4

m∠6=(1/8)(160°)=20°