Question

Question

In a diagram, ∠A
and ∠B
are vertical angles, and ∠B
is a complementary angle with ∠C
. If m∠A=22°
, write an equation that you can use to solve for m∠C for a 7th grader

Answer 1

To solve for \( m\angle C \), let's break down the information given:

1. Vertical Angles: \( \angle A \) and \( \angle B \) are vertical angles. This means they are equal in measure, so: \[ m\angle A = m\angle B \]

2. Complementary Angles: \( \angle B \) and \( \angle C \) are complementary angles, which means that the sum of their measures equals 90 degrees: \[ m\angle B + m\angle C = 90^\circ \]

Now, we know that \( m\angle A = 22^\circ \), so we can substitute this value into the equation for vertical angles: \[ m\angle B = 22^\circ \]

Now, we can plug this value into the complementary angles equation: \[ 22^\circ + m\angle C = 90^\circ \]

Now, we can rewrite this as an equation to solve for \( m\angle C \): \[ m\angle C = 90^\circ - 22^\circ \]

So the equation you can use to solve for \( m\angle C \) is: \[ m\angle C = 90^\circ - m\angle B \] or \[ m\angle C = 90^\circ - 22^\circ \]

This simplifies to: \[ m\angle C = 68^\circ \]

So, the equation is: \[ m\angle C = 90^\circ - 22^\circ \]