[tex]\bold{Figure\:1}:[/tex]
1. [tex]\sf{mUV = 32 + 70 = \underline{102°}}[/tex]
2. [tex]\sf{m∠VTZ = 32 + 88 = \underline{120°}}[/tex]
3. [tex]\sf{m∠LUTY = 70 + 92 = \underline{162°}}[/tex]
4. [tex]\sf{m VY = \underline{92°}}[/tex]
5. [tex]\sf{m∠LUTZ = 70 - 92 - 88 = \underline{110°}}[/tex]
[tex]\bold{Figure\:2}:[/tex]
1. [tex]\boxed{\sf{ 100°}}[/tex]
[tex]\mathcal{SOLUTION}:[/tex]
[tex]\sf{MPR = 2m∠PAR}[/tex]
[tex]\sf{MPR = 2 × 35 = 70°}[/tex]
[tex]\sf{MAP = m360 - MPR - MRY - MAY}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{360 - 105 - 85 - 70}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{360 - 260}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{100°}[/tex]
2. [tex]\boxed{\sf{52.5°}}[/tex]
[tex]\mathcal{SOLUTION}:[/tex]
[tex]\sf{m∠YRA = \frac {1}{2}mAY}[/tex]
[tex]\sf{=}[/tex] [tex]\sf\frac{1}{2}[/tex] [tex]\sf{(105)°}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{52.5°}[/tex]
3. [tex]\boxed{\sf{50°}}[/tex]
[tex]\mathcal{SOLUTION}:[/tex]
[tex]\sf{m∠AYP = \frac{1}{2} m∠PA}[/tex]
[tex]\sf{=}[/tex] [tex]\frac{1}{2}[/tex] [tex] \sf{×\:100 = 50°}[/tex]
4. [tex]\boxed{\sf{mPR = 70°}}[/tex]
5. [tex]\boxed{\sf{95°}}[/tex]
[tex]\mathcal{SOLUTION}:[/tex]
[tex]\sf{m∠RPA = m∠YPA + m∠YPR}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{\frac {1}{2} mAY + \frac {1}{2} mRY}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{\frac {1}{2}(105)° + \frac {1}{2} × 85°}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{\frac {1}{2} (105+85) = \frac {1}{2} × 190}[/tex]
[tex]\sf{=}[/tex] [tex]\sf{95°}[/tex]
#CarryOnLearning
