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For letter c do i have to make it equal 180

For letter c do i have to make it equal 180-example-1
User ZakW
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1 Answer

5 votes

Solution:

Given:


\begin{gathered} BP\text{ bisects }\angle ABC \\ m\angle ABP=34^0 \end{gathered}

An angle bisector is a line that divides an angle into two congruent angles.

This means line BP divides the measure of angle ABC into two equal angles.

The sketch below illustrates the angles.

The measure of ABC.


\begin{gathered} \angle ABC=\angle ABP+\angle PBC \\ S\text{ ince, BP bisects }\angle ABC,\text{ then ABP is half of ABC} \\ \angle ABP=(1)/(2)*\angle ABC \\ 34=(1)/(2)*\angle ABC \\ \text{Cross multiplying to get the angle,} \\ \angle ABC=34*2 \\ \angle ABC=68^0 \end{gathered}

Therefore, the measure of ABC is 68 degrees.

The measure of PBC.


\begin{gathered} BP\text{ bisects }\angle ABC\text{ into two equal angles} \\ \text{The angles forms from the bisection are }\angle ABP\text{ and }\angle PBC \\ \text{Hence,} \\ \angle ABP=\angle PBC \\ \\ m\angle ABP=34^0 \\ Si\text{ nce }\angle ABP=\angle PBC,\text{ then} \\ m\angle PBC=34^0 \end{gathered}

Therefore, the measure of angle PBC is 34 degrees.

For letter c do i have to make it equal 180-example-1
User Yngwietiger
by
3.9k points