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Question Number 172392 by greougoury555 last updated on 26/Jun/22

Commented by Rasheed.Sindhi last updated on 26/Jun/22

$$\theta =125°$$

Commented by mr W last updated on 26/Jun/22

$$yes!$$

Answered by sahiljakharjaat last updated on 26/Jun/22

Commented by som(math1967) last updated on 26/Jun/22

$$\varphi +\gamma =\frac{330}{2}=165$$$$\Rightarrow \theta =360-70-165=125$$

Answered by mr W last updated on 26/Jun/22

$$2\alpha +(2\beta -40)=180$$$$\Rightarrow \alpha +\beta =110$$$$$$$$2\varphi +(\beta -40)=180$$$$\Rightarrow \varphi =110-\frac{\beta }{2}$$$$similarly$$$$\Rightarrow \gamma =110-\frac{\alpha }{2}$$$$\Rightarrow \varphi +\gamma =2\times 110-\frac{\alpha +\beta }{2}=220-\frac{110}{2}=165$$$$$$$$\varphi +\gamma =({\theta }_1+{\phi }_1)+({\theta }_2+{\phi }_2)=({\theta }_1+{\theta }_2)+({\phi }_1+{\phi }_2)=\theta +40$$$$\theta +40=165$$$$\Rightarrow \theta =125✓$$

Commented by mr W last updated on 26/Jun/22

Commented by Tawa11 last updated on 26/Jun/22

$$\mathrm{Great}\mathrm{sir}$$

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