Question

if m∠tuv = 176° and m∠tul = 21°, find m∠luv.

Explanation:

Step1: Identify angle addition postulate

The measure of ∠TUV is the sum of ∠TUL and ∠LUV. So, \( m\angle TUV = m\angle TUL + m\angle LUV \).

Step2: Rearrange to solve for \( m\angle LUV \)

Subtract \( m\angle TUL \) from both sides: \( m\angle LUV = m\angle TUV - m\angle TUL \).

Step3: Substitute given values

Given \( m\angle TUV = 176^\circ \) and \( m\angle TUL = 21^\circ \), so \( m\angle LUV = 176^\circ - 21^\circ \).

Step4: Calculate the result

\( 176 - 21 = 155 \), so \( m\angle LUV = 155^\circ \).

Answer:

\( 155^\circ \)