Exercise 27 Page 593

According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180^(∘). However, in this case the sum of the interior angles has been equated with 360^(∘) instead of 180^(∘). The correct equation is as follows. 115^(∘)+39^(∘)+m∠ 1=180^(∘) By solving this equation, we can find m∠ 1.

115^(∘)+39^(∘)+m∠ 1=180^(∘)

AddTerms

Add terms

154^(∘)+m∠ 1=180^(∘)

SubEqn

LHS-154^(∘)=RHS-154^(∘)

m∠ 1=26^(∘)

The measure of ∠ 1 is 26^(∘).