Question

Find m/QRS if m/LRS= 40x, m/QRS = 1 + 67x, and m/QRL = 55°.

Answer 1

The value  of m/QRS  is 135°

What are adjacent angles?

Adjacent angles are two or more angles having:

• A common vertex
• A common side
• Do not overlap
• A non-common arm on the sides of the common arm.
• Are either supplementary or complementary based on the sum of the measures of angles.

Given the angles as;

• m/LRS= 40x,
• m/QRS = 1 + 67x
• m/QRL = 55°.

This is expressed as;

m/QRS  = m/LRS + m/QRL

Substitute the values

1 + 67x =  40x +   55°

collect like terms

27x = 54

Make 'x' the subject of formula

x = 54/ 27

x = 2

But :

m/QRS = 1 + 67x = 1 + 67(2) = 1 + 134 = 135°

Thus, the value  of m/QRS  is 135°

Learn more about adjacent angles here:

brainly.com/question/25713164

#SPJ1