Question

S is in the interior of ∠RQT. m∠RQS=(4x-20)°,m∠SQT=(3x+14)°, and m∠RQT=155°

Answer 1

Explanation:

Since we are not told what to look for, we can as well look for the value of x, m∠SQT and m∠RQS

Given

m∠RQS=(4x-20)°

m∠SQT=(3x+14)°

m∠RQT=155°

The addition postulate is true

m∠RQT= m∠RQS + m∠SQT

Substitute the given parameters into the formula

155 = 4x-20+3x+14

155 = 7x-6

7x = 155+6

7x = 161

x = 161/7

x = 23

Solve for m∠RQS

m∠RQS = 4x-20

m∠RQS = 4(23)-20

m∠RQS = 92-20

m∠RQS = 72°

Solve for m∠SQT

m∠SQT = 3x+14

m∠SQT = 3(23)+14

m∠SQT = 69+14

m∠SQT = 83°