Question

What is the measure of angle QRS

Answer 1

145=4y+y { exterior angle of triangle is equal to the sum of its opposite interior angle}

• 5y=145
• y=145/5
• y=29°

measure of / Q =4y =4×29=116°

measure of angleQRS

let unknown angle be'x'

• x+4y+y=180°{sum of angle of triangle}
• x+116°+29=180
• x=180-145
• x=35°

hope it helps

stay safe healthy and happy.

Answer 2

∠QRS = 35°

∠Q = 116°

Explanation:

∠QRS and ∠QRT are supplementary angles

Supplementary angles add up to equal 180

Thus, 145° + ∠QRS = 180

180 - 145 = 35

145 - 145 cancels out

we're left with ∠QRS = 35°

In order to find the measure of ∠Q

We must find y

We have already identified that ∠QRS = 35°

Which means that we can find y by using the triangle angles rule which states that all angles in a triangle add up to equal 180

So 180 = y + 4y + 35

now we solve for y

step 1 combine like terms

y + 4y = 5y

we now have 180 = 5y + 35

step 2 subtract 35 from each side

180 - 35 = 145

35 - 35 cancels out

now we have 145 = 5y

step 3 divide each side by 5

5y / 5 = y

145 / 5 = 29

We're left with y = 29

Now we can find ∠Q

To do this we substitute y for 29

∠Q = 4(29)

4 * 29 = 116

Hence ∠Q = 116