Answer:
[tex]\theta = 56[/tex]
Step-by-step explanation:
Represent the angles with [tex]\theta[/tex] and [tex]\alpha[/tex]
Such that:
[tex]\theta = 22 + \alpha[/tex]
Since both angles are complementary, we have:
[tex]\theta + \alpha = 90[/tex]
Substitute [tex]\theta = 22 + \alpha[/tex]
[tex]22 + \alpha + \alpha = 90[/tex]
[tex]22 + 2\alpha = 90[/tex]
Collect Like Terms
[tex]2\alpha = 90 - 22[/tex]
[tex]2\alpha = 68[/tex]
[tex]\alpha = 68/2[/tex]
[tex]\alpha = 34[/tex]
Recall that:
[tex]\theta = 22 + \alpha[/tex]
[tex]\theta = 22 + 34[/tex]
[tex]\theta = 56[/tex]
Hence:
The larger angle is 56
