Exercise 26 Page 518

We want to find the measure of ∠ ACB. Let's analyze the given rhombus.

In a rhombus, each diagonal bisects a pair of opposite angles. This means that the diagonal BD bisects ∠ ABC, and therefore m∠ ABD=m∠ CBD.

Recall the Interior Angles Theorem.

Interior Angles Theorem

The sum of the interior angles of a triangle is 180^(∘).

Let's consider the sum of the interior angles of △ BPC. m∠ PBC+ m∠ CPB +m∠ ACB=180 ⇕ 24+ 90 +m∠ ACB=180 Let's solve the equation.

24+90+m∠ ACB=180

AddTerms

Add terms

114 +m∠ ACB=180

SubEqn

LHS-114=RHS-114

m∠ ACB = 66

The measure of ∠ ACB is 66 degrees.